Special Sessions

As in previous editions of CEDYA / CMA, part of the conference is dedicated to special sessions, which address a topic of current interest in applied mathematics. So far, the organization has accepted the following proposals for special sessions:

List of Special Sessions

1 Advances in Time Stepping Methods

  • Organizers: Luis Rández (Universidad de Zaragoza), Juan Ignacio Montijano (Universidad de Zaragoza), Inmaculada Higueras (Universidad Pública de Navarra)

  • Section: Numerical Analysis and Numerical Simulation

  • Speakers:

    • Andrés Arrarás/Laura Portero (Universidad Pública de Navarra): "Reducing the splitting error of time-splitting methods for parabolic problems"

    • Fernando Casas (Universitat Jaume I) "High order splitting methods for the Vlasov-Poisson equation"

    • Teo Roldán (Universidad Pública de Navarra) "Implicit-explicit Runge-Kutta methods with low-storage requirements"

    • Juan Ignacio Montijano (Universidad de Zaragoza) "Exponential fitting techniques for the solution of stiff problems with a gap"

    • Soledad Pérez-Rodríguez (Universidad de La Laguna) "Some interesting 3-stage ROW methods"

    • Luis Rández (Universidad de Zaragoza) "On the construction of Hermite-Birkhoff-Taylor schemes"

    • Inmaculada Higueras (Universidad Pública de Navarra) "Optimized strong stability preserving IMEX Runge-Kutta methods"

  • Abstract: The goal of this special session is to show the most recent results on time stepping integrators for differential problems. These problems arise in different contexts, either directly or after the spatial discretization of partial differential equations.

    Some results on different aspects of numerical methods for differential problems will be presented, paying special attention to the efficient integration of problems arising in different applications

2 Analysis of mathematical models applied to epidemiological processes

  • Organizers: Begoña Cantó Colomina, Elena Sánchez Juan (Universitat Politècnica de València)

  • Section: Other topics: ‘Mathematical models in Epidemiology’

  • Speakers:

    • Santiago Alonso-Quesada (Universidad del País Vasco) "Analysis of a discrete-time SEIR epidemic model under a periodic impulse vaccination"

    • Joan Saldaña (Universidad de Girona) "Preventive behavioural responses and information dissemination in network epidemic models"

    • A. Benjamin Ivorra, B. Diène Ngom and C. Ángel M. Ramos (Universidad Complutense de Madrid): "A deterministic mathematical model to predict the risk of human diseases spread between countries. Application to the 2014-15 Ebola Virus Disease epidemic"

    • Begoña Cantó, Carmen Coll y Elena Sánchez (Universitat Politècnica de València) "On the equilibrium points in process of indirect transmission"

    • Begoña Cantó, Carmen Coll y Elena Sánchez (Universitat Politècnica de València) "Analysis of infections in seasonal epidemiological models"

  • Abstract: Mathematical modeling is a powerful tool for the development of research in applied sciences in the field of health: biomedicine, epidemiology, etc. When a bacterium or a virus in a population appears causing infection, the disease progression is analyzed by dynamic models that represent the growth of the different classes in which the population is distributed, for example, susceptible infected population, and the recovered population, leading to analyze whether the disease will be eradicated, or otherwise, will remain endemic or produce a pandemic.

    Usually, these models are described by differential equations, difference equations or contact network. Matrix analysis techniques, control theory and network theory, play an important role in the development of epidemiological models.

    In this special session some of these methods will be presented in order to give an overview of some different approaches and therefore certain different mathematical tools that are useful to address a problem describing the evolution of infectious disease are presented.

    For instance, if the structure of infectious disease contact is modeled by a network of contacts, the epidemiological process can be studied using network theory. In particular, given that the responses of human behavior have a significant impact on the spread of epidemics, you can add another network that incorporates preventive responses that can be taken by individuals. This second network that models the information, has the same set of nodes that the contact network. This approach leads to epidemic analysis models in which the epidemic threshold is expressed as a function of the overlap of the two networks.

    In this session the study of epidemiological processes under the focus of control theory will also be addressed. Obtaining the equilibrium points (one free of disease and the other the point where the disease is endemic) and its local stability of an epidemic model in discrete time domain obtained by the discretization of a model set in continuous time. Besides the study of positivity, this research proposes the design of a control law (signal vaccination) with the aim of eradicating infectious disease of the host population. This vaccination signal is based on control theory developed for linearization of a nonlinear open loop system. In some infectious disorders, infection is not directly through contact with an infected individual, but by contact with environmental wastes. Consideration of environmental infection is done via a discrete model and can undertake the study of the number of basic playback, around the endemic stability point and the control of the evolution of the disease.

    Another field of work that allows the development of the study of epidemiological processes is the theory of matrices. The special structure of the coefficient matrix of the model allows to draw spectral properties and conclusions obtaining in this way certain valuable information on the epidemiological process. For example, you can consider an age-structured model where the probability of infection may depend or not on the age of the infecting individual or susceptible to be infected. Their study involves a matrix analysis of the transition matrices and infection.

3 Applied Mathematics in Architecture

  • Organizers: Enrique D. Fernández Nieto, Gladys Narbona Reina (Universidad de Sevilla).

  • Section: Applied Mathematics for Industry

  • Speakers:

    • Antonio Domínguez Delgado (Universidad de Sevilla) "Numerical evaluation of ventilated facades energy efficiency in Southern Spain"

    • M. Lourdes Tello Del Castillo (Universidad Politécnica de Madrid) "On a green roof mathematical model"

    • Macarena Gómez Mármol (Universidad de Sevilla) "Reduced Bases Methods. Application to thermal resoluction into the walls."

    • Francisco Ortega Riejos (Universidad de Sevilla) "Determining efficient routes of ecotourism in nature parks under environmental constraints"

    • J. Francisco Padial Molina (Universidad Politécnica de Madrid) "Modeling a double-glass windows with a water-flow inside"

    • Enrique Rodríguez Jara (Universidad de Cádiz) "Building and surroundings Thermal and Aeraulic coupling"

    • José Sánchez de la Flor (Universidad de Cádiz) "Potential energy savings in air-conditioning building systems, due to the improvement of outdoor air"

    • Carmen Galán Marín/Juan Rojas Fernández (Universidad de Sevilla) "Microclimatic simulation using Freefem++ for the desing of Eco-Eficient building"

  • Abstract: The main goal of this special session is to show different solutions or approaches to certain problems of interest in Architecture. Examples may include problems of energy efficiency, optimal design of buildings or applications in urban planning, among others. To study these problems, it is necessary to consier applications of mathematics in different areas, such as mathematical modeling, differential equations, numerical simulation, graph theory and control theory and optimization.

    The speakers in this special session are mathematical experts, architects and engineers. This is another goal: to meet people having a strong applied mathematics background with people from applied research in architecture and from different Spanish universities. We also want to meet both architects and engineers which collaborate with mathematicians to study different issues and research projects in Architecture. This will exchange knowledge on applications of interest, and different views to address this kind of problems and possible collaborations.

4 Boundary Conditions for Flow Problems

  • Organizer: Malte Braack (Universität Kiel, Germany)

  • Section: Numerical Analysis and Numerical Simulation

  • Speakers:

    • Roland Becker (Université Pau, France)
    • Rodolfo Bermejo (Universidad Politécnica de Madrid) "On the influence of slip-no slip and different outflow boundary conditions on high Reynolds number flows"
    • Franck Boyer (Aix-Marseille Université)
    • Malte Braack (Universität Kiel, Germany) "Stability of outflow conditions for Navier-Stokes"
    • Alfonso Caiazzo (Weierstraß-Institute für Angewandte Analysis und Stochastik, Berlin)
    • Juan Casado Díaz (Universidad de Sevilla)
    • Giulia Deolmi (RWTH Aachen) "Effective boundary conditions for compressible flows over a rough surface"
    • Gert Lube (Universtität Göttingen, Germany)
    • Tomáš Neustupa (Czech Technical University in Prague, Czech Republic) "Stationary flow through a cascade of profiles with an arbitrarily large inflow - The mathematical model, existence of a weak solution"
  • Abstract: Boundary conditions are essential for the formulation of partial differential equations. They are necessary to ensure existence and uniqueness of solutions. However, in many cases, the formulation of boundary conditions are not clear a priori, but they are part of the modeling. This makes the question of mathematical features even more important. Beside their theoretica properties the numerical treatment of boundary conditions are important as well. New numerical concepts comprise weakly implemented boundary conditions, Nitsche’s method, moving boundaries etc. This Special Session focuses on new analytical and numerical achievements of such aspects for the Navier-Stokes equations. The spectrum includes typical issues as e.g. outflow conditions, slip- and no-slip conditions, rough domains.

5 Continuous and Discrete Dynamical Systems

  • Organizers: Antonio Algaba (Universidad de Huelva), Jaume Giné (Universitat de Lleida)

  • Section: Dynamical Systems

  • Speakers:

    • Francisco Balibrea Gallego (Universidad de Murcia) "Generation and results on difference equations of Thue-Morse, Fibonacci and Shapiro"

    • Victoriano Carmona (Universidad de Sevilla) "Periodic orbits and global connections in reversible piecewise linear systems"

    • Isaac García (Universitat de Lleida) "Cyclicity of nilpotent centers with homogeneous nonlinearities"

    • Pedro Torres (Universidad de Granada) "Stability and chaos in the Kepler problem with variable mass"

    • Eduardo Liz (Universidade de Vigo) "The importance of harvest timing: Dynamic analysis of a discrete model"

    • Tere Martinez-Seara (Universitat Politècnica de Catalunya) "Regularization of local bifurcations in Filippov systems"

    • Rafael Obaya (Universidad de Valladolid) "Linear-quadratic control processes with time-dependent coefficients"

    • Cristóbal García García (Universidad Huelva) "Integrability of degenerate vector fields"

    • Emilio Freire (Universidad de Sevilla) "Singularity of Teixeira: a nonlinear analysis of the bifurcation behavior"

  • Abstract: Dynamical systems theory studies the evolution of processes described either by differential equations or by discrete transformations. We propose a special session in which the research, progress and results of researchers from different Spanish universities (usually in collaboration with foreign universities) are shown. The goal of this special session is to present some of the latest advances in this discipline and to encourage csollaboration among participants.

6 Evolution models with nonlocal terms: theory and numerical approximation

  • Organizers: María López-Fernández (Gran Sasso Science Institute, L’Aquila, Italia), Ángel Durán Martín (Universidad de Valladolid).

  • Sections: Numerical Analysis and Numerical Simulation, Partial Differential Equations

  • Speakers:

    • Francisco Javier Sayas (University of Delaware) "Time domain coupling of finite and boundary elements"
    • Ángel Castro (Universidad Autónoma de Madrid)
    • Francisco Gancedo (Universidad de Sevilla)
    • César Palencia (Universidad de Valladolid) "Time Runge-Kutta discretizations of abstract parabolic Volterra equations with bad initial data"
    • Jerónimo Rodríguez (Universidad de Santiago de Compostela) "Integral equations for 1D transient wave propagation"
    • Miguel Ángel López Marcos (Universidad de Valladolid) "Second-order numerical integration of a size-structured cell population model with equal fission"
    • Óscar Angulo (Universidad de Valladolid) "Second-order numerical integration of a size-structured cell population model with asymmetric division"
    • Eduardo Cuesta (Universidad de Valladolid) "Linear Volterra equations. Applications in satellite image classification"
  • Abstract: The goal of this special session is the theoretical and numerical analysis of some nonlocal evolution problems. Models associated with diverse applications will be considered, including problems in acoustics and electromagnetism, fluid dynamics, population dynamics and imaging. Some aspects of the corresponding modeling may require the inclusion of nonlocal terms, either in the form of evolution integral equations or affecting the dependence on spatial variables through nonlocal operators. The session aims to deepen in a better understanding of the model and also in an efficient numerical treatment.

7 Homogenization of Elliptic Equations

  • Organizer: Pedro J. Martínez-Aparicio (Universidad Politécnica de Cartagena, Murcia)

  • Section: Partial Differential Equations

  • Speakers:

    • Juan Casado (Universidad de Sevilla) "Two-scale convergence and random homogenization"
    • Daniela Giachetti (Sapienza Universitá di Roma) "Homogenization of semilinear elliptic problems singular at u = 0"
    • François Murat (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris VI) "Homogenization of the brush problem with a source term in L^1"
  • Abstract: The Theory of Homogenization dates back to the late sixties, it has been very rapidly developed during the last two decades, and it is now established as a distinct discipline within mathematics.

    Composites are materials that have inhomogeneities on length scales that are much larger than the atomic scale (which allows us to use the equations of classical physics at the lenght scales of the inhomogeneities) but which are essentially homogeneous at macroscopic lenght scales.

    Composite materials (e.g. fibred, stratified, crystalline, porous,...) play an important role in many branches of Mechanics, Physics, Chemistry and Engineering.

    The main problem is to determine macroscopic effective properties (for example heat transfer, elasticity, electric conductivity, magnetic permeability, flow, etc.) of strongly heterogeneous multiphase materials. A common feature in such problems is that the governing equations involve rapidly oscillating functions due to the heterogeneity of the underlying material, i.e. the physical parameters (such as conductivity, elasticity coefficients,...) are discontinuous and oscillate very rapidly between the different values characterizing each of the components.

    These rapid oscillations render a direct numerical treatment very hard or even impossible. Therefore one has to do some kind of averaging or asymptotic analysis. We may think to get a good approximation of the macroscopic behavior of such a heterogeneous material by letting the parameter ɛ, which describes the fineness of the microscopic structure, tend to zero in the equations governing phenomena such as heat conduction and elasticity. It is the purpose of homogenization theory to describe these limit processes, when ɛ tends to zero.

    More precisely, homogenization deals with the asymptotic analysis of Partial Differential Equations of Physics in heterogeneous materials with a periodic structure, when the characteristic length ɛ of the period tends to zero.

8 Hyperbolic PDEs: Numerical Methods and Applications

  • Organizers: José M. Gallardo (Universidad de Málaga), Pep Mulet (Universitat de València)

  • Section: Numerical Analysis and Numerical Simulation

  • Speakers:

    • Antonio Baeza Manzanares (Universitat de València) "Finite difference WENO and Adaptive Mesh Refinement techniques for Vlasov-Maxwell equations"

    • Isabel Cordero Carrión (Universitat de València) "Minimally implicit Runge-Kutta methods for hyperbolic equations with stiff source terms"

    • José Manuel González Vida (Universidad de Málaga) "Efficient GPU implementation of a two waves TVD-WAF method for the two-dimensional one layer Shallow Water system and its validation for tsunami forecasting"

    • Enrique Fernández Nieto (Universidad de Sevilla) "A coupled duality/finite volume method for 2D shallow viscoplastic avalanches models"

    • Cipriano Escalante Sánchez (Universidad de Málaga) "Weakly dispersive shallow water flows: hybrid finite-volume finite-difference schemes"

    • Francisco Guerrero Cortina (Universitat de València) "Finite difference WENO schemes for multi-dimensional porous media flows"

    • Arturo Hidalgo (Universidad Politécnica de Madrid) "ADER-WENO Finite Volume Schemes with Adaptive Mesh Refinement for Hyperbolic Problems"

    • David Zorío Ventura (Universitat de València) "Boundary extrapolation techniques for finite difference schemes for complex geometries"

  • Abstract: A significant number of phenomena arising in different scientific areas can be modeled by first-order hyperbolic PDEs systems: geophysical flows, gas dynamics, acoustics and so on. Typically, such systems arise from neglecting diffusive or dispersive terms in the equations, which are of higher order but relatively smaller than the convective first order terms. Obtaining good numerical approximations to solutions of such systems is crucial, since analytical solutions are usually unavalaible because of the nonlinear nature of the equations.

    Due to the development of solution discontinuities in nonlinear hyperbolic systems, numerical methods for approximate solution must possess certain characteristics. In this special section a series of works will be presented dealing on different aspects of desing and analysis of such numerical schemes, with special emphasis on obtaining conservation and high order properties. Also applications of such schemes to certain problems based on real systems will be shown.

9 Mathematical Models for Computer Science

  • Organizer: Jesús Medina Moreno (Universidad de Cádiz)

  • Section: Other topics 'Applied Mathematics for Computer Science'

  • Speakers:
    • Nicolás Madrid (University of Ostrava, Czech Republic) "Idempotent Morphology Dilations"
    • M. Romero and Juan Luis Castro (Universidad de Granada) "From tags cloud to concepts cloud"
    • Juan Moreno (Universidad de Castilla-La Mancha, Spain) "Efficient representation of fuzzy membership functions for applications"
    • Manuel Ojeda-Aciego (Universidad de Málaga) "On the definition of suitable orderings to generate adjunctions over an unstructured codomain"
    • Pablo Cordero (Universidad de Málaga) "Multilattices and residuated multilattices: generalizing lattice theory"
    • María Eugenia Cornejo, Jesús Medina Moreno y Eloísa Ramírez-Poussa (Universidad de Cádiz) "Reducing concept lattices by cuts"
  • Abstract: Fundamental mathematical tools need to be developed in order to model interesting problems arisen in Computer Science. The purpose of this Special Session is to provide an international forum for presentation of recent results and advances in these important tools. The not exhaustive list of topics includes:

    • General operators useful in Computer Science
    • Aggregation functions
    • Aggregations for extensions of fuzzy sets
    • Fuzzy sets and fuzzy logic
    • Logic programming
    • Rough sets
    • Fuzzy rough sets
    • Interval-valued fuzzy sets
    • Formal concept analysis
    • Fuzzy measures and integrals

10 Modeling and Simulation in Sedimentary Processes

  • Organizers: Manuel J. Castro Díaz, Enrique D. Fernández Nieto, Tomás Morales de Luna

  • Section: Numerical Analysis and Numerical Simulation

  • Speakers:

    • Ángel Balaguer (Universidad Politécnica de Valencia) "Numerical-experimental modelling of sediment transport problems using a high-order finite volume scheme"

    • Tomás Morales de Luna (Universidad de Córdoba) "Sediment transport in shallow water: improvement of bedload and suspended transport"

    • Pep Mulet (Universidad de Valencia) "Implicit-Explicit Runge-Kutta methods for polydisperse sedimentation models with compression"

    • Gladys Narbona Reina (Universidad de Sevilla) "On a new derivation of the Saint-Venant-Exner model with energy balance"

    • Carmen Zarzuelo (Andalusian Institute for Earth System Research. Granada) "Modeling sediment transport induced by tidal currents and wind waves in Cádiz Bay"

    • Marc de la Asunción (Universidad de Málaga) "Efficient implementation of bedload sediment transport finite volume models over non-structured meshes"

  • Abstract: Phenomena related to transport of sediments have a huge interest, since they decisively affect the human beings and the Earth's morphology. Evolution of sediment is of vital importance in conservation, development and use of land and water resources, and therefore the analysis and prediction are essential for prevention and avoiding natural end environmental disasters. It is also essential to perform intelligent approaches that allow the correct use of resources.

    One of the main disadvantages of the study of sediment transport is its timescale, which can be very variable depending on the type of phenomenon to observe. Thus, erosion and sediment that occur as a consequence of a watercourse overflow has nothing to do with the slow evolution processes related to the marine coast, reservoirs or rivers.

    From the viewpoint of mathematical modeling and numerical simulation, there are also many difficulties. One of them, in numerical simulation of sediment transport problems, is due to the difference between the flow characteristic speed and sediment transport. On the other hand, first order methods introduce a big diffusion in the sediments layer, making it necessary to consider high order methods in order to obtain an accurate numerical solution.

    There is a lot of literature related to the modeling of sedimentary processes, from drag erosion models and deposition problems, to polydisperse sedimentary processes, where are taken into account the different types of density and diameter of the sediment type, as well as the various forces involved in the mixture of solid and fluid particles.

    This special session features specialists in both modeling and numerical simulation of different types of sedimentary processes. We intend to get an overview of the latest advances developed by participants as well as possible future collaborations.

11 Non-Autonomous Dynamical Systems and Applications

  • Organizers: María José Garrido Atienza (Universidad de Sevilla), Tomás Caraballo Garrido (Universidad de Sevilla), José Valero Cuadra (Universidad Miguel Hernández)

  • Section: Dynamical Systems

  • Speakers:

    • María José Garrido Atienza (Universidad de Sevilla) "Random attractors for retarded stochastic PDEs"

    • Marta Herrera Cobos, Universidad de Sevilla "Non-autonomous nonlocal parabolic equations"

    • Antonio Miguel Márquez Durán (Universidad Pablo de Olavide, Sevilla) "Asymptotic behavior for a non-classical and non-autonomous diffusion equation containing some hereditary characteristic"

    • Francisco Morillas Jurado (Universidad de Valencia) "Graduation of life tables: from static to dynamic application"

    • Sylvia Novo (Universidad de Valladolid) "Uniform persistence for monotone skew-product semiflows with applications to neural networks"

    • Rosana Rodríguez López (Universidad de Santiago de Compostela) "On the existence of solutions to fractional differential equations with unbounded nonlinearity"

    • José Valero (Universidad Miguel Hernández, Elche), "New results on the structure of the attractor for reaction-diffusion equations without uniqueness"

  • Abstract: The aim of this session is to offer an overview on recent results concerning the asymptotic behavior of solutions of non-autonomous partial and ordinary differential equations. Some of the main topics, but not the only ones, in this session are: asymptotic dynamics of non-autonomous dynamical systems, in particular, existence and properties of attractors for non-autonomous equations, stability, stabilization, attractors for equations without uniqueness of solutions, dynamics of equations with delay, and finite-dimensional dynamics for infinite dimensional dynamical systems.

12 Numerical Acoustics

  • Organizer: Francisco-Javier Sayas (University of Delaware, USA)

  • Section: Numerical Analysis and Numerical Simulation

  • Speakers:

    • Julien Diaz (INRIA, France) "High-order Discontinuous Galerkin approximations for elasto-acoustic scattering problems"

    • Víctor Domínguez (Universidad Pública de Navarra, Spain) "High order Nystrom methods for transmission problems for Helmholtz Equation"

    • Andrea Moiola (University of Reading, U. K.) "Trefftz-discontinuous Galerkin methods for the wave equation"

    • Peter Monk (University of Delaware, USA) "Time dependent scattering from diffraction gratings"

    • Daniel Peterseim (Universität Bonn, Germany) "Eliminating the pollution effect in Helmholtz problems by local subscale correction"

  • Abstract: The goal of this special session is to bring together experts in different areas of the numerical analysis and simulation of problems in linear acoustics, with an empahsis on scattering of waves. The topics include time and frequency domain problems, volume and integral methods, as well as direct and inverse problems. There has been much recent progress in the area of integral equation methods for scattering problems. Linear acoustic waves have been widely studied for their own sake (with a large number of practical applications in physics and engineering), and also as a stepping stone towards understading more complex waves, like seismic (elastic) and electromagnetic waves. In particular, high frequency problems and transient problems have received much attention in the past decade. The field has also been enriched in the attention to complex phenomena, that require much more theoretical and computational effort than the traditional model problems of scattering by impenetrable obstacles. In particular, there is interest in coupling procedures using integral equation formulations (Boundary Element Methods) for different materials, in mixing integral models with variational schemes such as Finite Elements, or in scattering by periodic gratings.

    The special session would bring well-established researchers in the area of Numerical Analysis for Waves with younger up-and-coming researchers in the field. They represent a wide array of research techniques in the area, with a well balanced act between mathematical rigor and practical computation.

13 Optimal Control of Partial Differential Equations

  • Organizers: Eduardo Casas (University of Cantabria), Konstantinos Chrysafinos (National Technical University of Athens)

  • Section: Control and Optimization

  • Speakers:

    • Eduardo Casas (Universidad de Cantabria) "The Velocity Tracking Control Problem for the Evolutionary Navier-Stokes Equations"

    • Enrique Fernández Cara (Universidad de Sevilla) "Three results concerning the controllability of PDEs"

    • Francisco Javier Fernández Fernández (Centro Universitario de la Defensa, Universidade de Vigo) "Optimal control of urban heat islands"

    • Michael Hintermüller (Humboldt Universität zu Berlin) "Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state"

    • Mariano Mateos (Universidad de Oviedo) "Numerical approximation of state constrained Dirichlet control problems"

    • Ira Neitzel (Technische Universität München) "Finite element error estimates for nonconvex parabolic control problems with gradient constraints"

    • Arnd Rösch (Universität Duisburg-Essen) "Optimal control of a chemotaxis problem"

    • Konstantinos Chrysafinos (National Technical University of Athens) "Stability estimates for fully-discrete approximations of the Allen-Cahn equations and applications to optimal control"

  • Abstract: The goal of this section is to gather some researchers in optimal control of partial differential equations that will present the latest results in the field. The talks will deal with theory, numerics and applications. Concerning the theoretical results, sparsity and second order analysis are two very active research lines at the moment. Second order analysis is the main tool to prove error estimates in the discretization of nonconvex control problems or in the study of stability of the solutions with respect to perturbations in the data. This topic has been developed in the last years, but there are still many open problems.

    Sparsity is another topic that have focused the attention of many specialists in optimal control. In the control of distributed parameter systems, usually we cannot put control devices at every point of the domain. Actually, we are allowed to use small regions to put the controllers. Then the big issue is which region is the most convenient to localize them. Of course, we have to determine the power of the controllers as well. These controls are called sparse because they are not zero only in a small region of the domain.

    Of course, the numerical analysis is an essential issue in the control of partial differential equations. The numerical solution of optimal control problems governed by partial differential equations requires a suitable discretization of the equation and a related approximation of the state and control functions. For instance, finite element or more general Galerkin methods are applied, that are based on grids for the spatial or time domains. The smaller the mesh sizes of these grids are, the larger is the dimension of the resulting discretized optimal control problems. It is a characteristic difficulty in the control of partial differential equations that the dimension of the discretized problems easily becomes very large. An important question naturally arises: How fine the discretization of the problem must be in order to reach a desired precision of its solution? Therefore, there is a natural interest in estimating the distance of the optimal solution of the discretized control problem to the exact optimal solution of the continuous one. The main question is to estimate the order of this distance, i.e. the approximation error, in terms of the mesh sizes. After first contributions to this issue for linear elliptic and parabolic equations, the associated research became very active in the last decade. Problems of increasing level of difficulty were investigated. Recently, control problems for quasilinear elliptic equations and for parabolic equations received more attention. Moreover, problems with given pointwise state constraints are investigated actively. Here, the treatment of the Lagrange multipliers is the main difficulty.

    Finally, applications of control theory to fluid dynamics problems described by Navier-Stokes equations or some other nonlinear partial differential equations, reaction-difussion problems, magentism problems, etc. are actively studied nowdays.

    This session deals with the most recent results about these issues.

14 Structured Matrices and Numerical Linear Algebra

  • Organizers: Rafael Cantó (Universitat Politècnica de València), Juan Manuel Peña (Universidad de Zaragoza)

  • Section: Numerical Linear Algebra

  • Speakers:

    • Pedro Alonso (Universidad de Oviedo). "Characterizations of Almost Strictly Sign Regular matrices and some particular cases."

    • Rafael Bru (Universitat Politècnica de València) "Preconditioners and iterative methods for solving linear systems."

    • Yasmina Khiar (Universidad de Zaragoza) "Matrix analysis of the Newton interpolation formula."

    • José Javier Martínez (Universidad de Alcalá) "Polynomial least squares fitting by using the Bernstein basis."

    • Ana María Urbano (Universitat Politècnica de València) "An application of the Modified Gram-Schmidt Algorithm."

  • Abstract: Structured matrices form a subject of growing interest and importance in the numerical analysis and applied and numerical linear algebra. They typically lead to the development of adapted numerical methods and theoretical understanding of diverse concepts in statistics, optimization, economics or approximation, among other fields. In this special session we assemble five talks on different types and applications of structured matrices. Particular attention will be paid to the study of iterative methods for solving linear systems Ax=b, where A is an structured matrix (M-matrix, H-matrix, symmetric definite positive, ...) using Krylov methods and their preconditioners. In other talk, the modified Gram-Schmidt process (MGS) is considered to improve the condition numbers for the eigenvalues of a given matrix. Another talk will present some recent advances for the class of structured matrices called almost strictly sign regular matrices. Least squares approximation using the Bernstein basis and its corresponding Bernstein-Vandermonde matrices will be considered in another talk. Finally, a talk will be devoted to matrix tools related with Newton formula for polynomial interpolation, including factorizations of Vandermonde and Bernstein-Vandermonde matrices.

15 Some Successful Collaborations with Industry Developed by Math-In Members

  • Organizer: Peregrina Quintela Estévez (Red Española Matemática-Industria (Math-In))

  • Section: Applied Mathematics for Industry

  • Speakers:

    • Peregrina Quintela Estévez (Red Española Matemática-Industria (Math-In)) "Numerical simulation of lashing for granite sheets ensuring the safety in marine transport"

    • Dolores Gómez Pedreira (Universidade de Santiago de Compostela) "Thermo-electromagneto-hydrodynamic numerical simulation of the removal of volatile impurities in molten silicon"

    • José Durany Castrillo (Universidade de Vigo) "A new low-cost technology for biothermal behavior of human foot and footwear through mathematical models."

    • Carlos Vázquez Cendón (Universidade da Coruña) "Mathematical transfer to life insurance companies: ALM modelling and its implementation in GPUs"

  • Abstract: The minisymposium "Some success collaborations with Industry developed by Math-In members" will emphasize the importance of the mathematical methods and techniques in the resolution of industrial problems. In particular, four success stories between research groups in Industrial Mathematics and companies will be presented. To show the great potential for innovation of Mathematical technology, four different sectors of economic activity will be involved: Transport, Materials, Biotechnology and Finances. Each speaker will explain the improvements to achieve a successful implementation in companies.

16 Application of Numerical Modelling in Oceanography and Meteorology

  • Organizers: Miguel Bruno Mejías (Universidad de Cádiz), Jorge Macías Sánchez (Universidad de Málaga)

  • Section: Other Topics: Other Topics: 'Numerical Simulation in Oceanography and Meteorology'

  • Speakers:
    • Diego Macías Moy (European Commision Joint Research Center)

    • Alfredo Izquierdo González (Universidad de Cádiz)

    • Vicente Pérez (Meteogalicia)

    • Javier Delgado (Universidad de Málaga)

  • Abstract: Numerical modeling of meteorological processes is an activity that has long been applied fairly routine in social life. Although it is not so in the case of oceanographic processes modeling, it is decisive its use to address certain specific problems related, for example, to predict the evolution of accidental discharges at the sea and maritime rescue work.

    Although there is a need to use these simulation models in operational tasks to predict how will evolve the different physical processes, it is evident, many times, that we find limitations and lack of confidence in the predictions we do with them. This need for their use becomes mandatory the continue improving of these models where is essential the participation of both, physical and mathematical approaches. Improved numerical integration methods performed in a mathematical context, aimed to achieve numerical schemes mores stables and more efficient boundary conditions help that predictions be more accurate. This activity in improving the available numerical models also clearly depends on the quality of the observed geophysical variables used in the experimental validation of the models.

    In addition to this immediate demand for forecasts produced by numerical models today's society need to use models to predict changes in the different atmospheric and oceanic variables caused by the process of climate change that is experiencing the planet. Of particular interest in this latter area is the modeling of the biological response of the ocean to changes forced by atmospheric and hydrodynamic conditions. The purpose of this session is to provide cutting edge on the involvement of the applications of numerical modeling in helping to develop these activities.

17 Reductions of Differential Equations

  • Organizer: Mª Concepción Muriel Patino (Universidad de Cádiz)

  • Section: Ordinary and Partial Differential Equations

  • Speakers:

    • Paola Morando (University of Milan) "Solvable structures in determination of invariant solution to PDEs"

    • Mª Concepción Muriel Patino (University of Cádiz) "Some connections between generalized symmetries and lambda-symmetries for second-order ordinary differential equations"

    • Adrián Ruíz Serván (University of Cádiz) "Solvable structures and integrability by quadratures of third-order ordinary differential equations admitting the non-solvable symmetry algebra sl(2,R)"

    • José Ramírez Labrador (University of Cádiz) "A reduction method for polynomial ordinary differential equations and applications"

    • Juan Manuel Vidal Pérez (University of Cádiz) "A lambda-symmetry algorithm in Maple for the integrability of second-order ordinary differential equations"

  • Abstract: This session is devoted to reduction problems of differential equations. Theory and applications of different approaches to find exact solutions to differential equations will be discussed. This includes, but not limited to, Lie symmetry analysis, λ − symmetries, μ − symmetries, σ − symmetries, solvable structures, linearization techniques by using local and nonlocal transformations, Prelle-Singer method, Jacobi last multipliers and others. Problems related to the design of computer programs for the algorithms of some of the methods will also be considered.