- Sevilla, Spain
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The aim of this paper is to prove the existence of a weak-renormalized solution to a simplified model of turbulence of the $k-\varepsilon$ kind in spatial dimension $N=2$. The unknowns are the average velocity field and pressure, the mean... more
The aim of this paper is to prove the existence of a weak-renormalized solution to a simplified model of turbulence of the $k-\varepsilon$ kind in spatial dimension $N=2$. The unknowns are the average velocity field and pressure, the mean turbulent kinetic energy and an appropriate time dependent variable. The motion equation and the additional PDE are respectively solved in the weak and renormalized senses.
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This paper deals with the solution of some multi-objective optimal control problems for several PDEs: linear and semilinear elliptic equations and stationary Navier-Stokes systems. Specifically, we look for Nash equilibria associated with... more
This paper deals with the solution of some multi-objective optimal control problems for several PDEs: linear and semilinear elliptic equations and stationary Navier-Stokes systems. Specifically, we look for Nash equilibria associated with standard cost functionals. For linear and semilinear elliptic equations, we prove the existence of equilibria and we deduce related optimality systems. For stationary Navier-Stokes equations, we prove the existence of Nash quasi-equilibria, i.e. solutions to the optimality system. In all cases, we present some iterative algorithms and, in some of them, we establish convergence results. For the existence and characterization of Nash quasi-equilibria in the Navier-Stokes case, we use the formalism of Dubovitskii and Milyutin. In this context, we also present a finite element approximation and we illustrate the techniques with numerical experiments.
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1. INTRODUCCION Ante todo, deseo mostrar mi agradecimiento a todas las personas que hicieron posible este curso y, muy en especial, al Secretario del mismo, Joaqúın Hernández Gómez, Catedrático del IES S. Juan Bautista (Madrid) y Profesor... more
1. INTRODUCCION Ante todo, deseo mostrar mi agradecimiento a todas las personas que hicieron posible este curso y, muy en especial, al Secretario del mismo, Joaqúın Hernández Gómez, Catedrático del IES S. Juan Bautista (Madrid) y Profesor Asociado de la Universidad Complutense, por los esfuerzos realizados. Los objetivos que se pretendieron alcanzar en este curso fueron principalmente dos: a) Por una parte, analizar de qué modo y en qué dosis es/seŕıa posible motivar la enseñanza de las Matemáticas en Secundaria a través de las aplicaciones. b) Por otra parte, comparar con los métodos y costumbres que tienen lugar en otros páıses europeos. En este año, declarado por la UNESCO Año Mundial de las Matemáticas, nos pareció indicado analizar la problemática ligada a la Educación Matemática desde todos los puntos de vista posibles. Este esṕıritu guió la confección del programa de este curso y la elección de los conferenciantes y participantes en las Mesas Redondas. El curso fue diseñado e...
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In this paper, we deal with the global exact controllability to the trajectories of the Boussinesq system. We consider 2D and 3D smooth bounded domains. The velocity field of the fluid must satisfy a Navier slip-with-friction boundary... more
In this paper, we deal with the global exact controllability to the trajectories of the Boussinesq system. We consider 2D and 3D smooth bounded domains. The velocity field of the fluid must satisfy a Navier slip-with-friction boundary condition and a Robin boundary condition is imposed to the temperature. We assume that one can act on the velocity and the temperature on an arbitrary small part of the boundary. The proof relies on three main arguments. First, we transform the problem into a distributed controllability problem by using a domain extension procedure. Then, we prove a global approximate controllability result by following the strategy of Coron et al [J. Eur. Math. Soc., 22 (2020), pp. 1625-1673], which deals with the Navier-Stokes equations. This part relies on the controllability of the inviscid Boussinesq system and asymptotic boundary layer expansions. Finally, we conclude with a local controllability result that we establish with the help of a linearization argument ...
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This paper deals with a strategy to solve numerically control problems of the Stackelberg--Nash kind for heat equations with Dirichlet boundary conditions. We assume that we can act on the system t...
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The computation of optimal profiles, i.e. those minimizing the drag, has been investigated by several suthors. frequently, the drag has been approximated by the viscous energy which is dissipated in the fluid. For instance, O. Pironneau... more
The computation of optimal profiles, i.e. those minimizing the drag, has been investigated by several suthors. frequently, the drag has been approximated by the viscous energy which is dissipated in the fluid. For instance, O. Pironneau computes in [9,10] the “derivative” of this quantity adapting Hadamard’s normal variations techniques. F. Murat and J. Simon use in [6] formal calculus to
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ABSTRACT This paper is devoted to analyzing the control of vicoelastic fluids of the Jeffreys kind, also known as Oldroyd models. We will present the interesting problems, with special emphasis in the difficulties that they involve. Then,... more
ABSTRACT This paper is devoted to analyzing the control of vicoelastic fluids of the Jeffreys kind, also known as Oldroyd models. We will present the interesting problems, with special emphasis in the difficulties that they involve. Then, we will consider appropriate linear approximations and we will establish some partial approximate-finite dimensional controllability results in an arbitrarily small time, with distributed or boundary controls supported by arbitrarily small sets. The proofs rely on some specific unique continuation properties which are implied by the structure of the solutions.
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Page 1. Numer. Math. 55, 33-60 (1989) Numerische Mathematik 9 Springer-Verlag 1989 The Convergence of two Numerical Schemes for the Navier-Stokes Equations Enrique Fernandez-Cara 1 and Mercedes Marin Beltran ...
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Research Interests: Mathematics, Applied Mathematics, Parallel Algorithms, Mathematical Programming, Numerical Analysis, and 14 moreConvergence, Applied Mathematics and Computational Science, Splitting, PARTIAL DIFFERENTIAL EQUATION, Parallel Algorithm, Numerical Analysis and Computational Mathematics, High Dimensionality, Parallelization, Differential equation, Fractional-step Method, Boundary Value Problem, Electrical And Electronic Engineering, Elliptic equation, and Iterative Method(Convergence, Applied Mathematics and Computational Science, Splitting, PARTIAL DIFFERENTIAL EQUATION, Parallel Algorithm, Numerical Analysis and Computational Mathematics, High Dimensionality, Parallelization, Differential equation, Fractional-step Method, Boundary Value Problem, Electrical And Electronic Engineering, Elliptic equation, and Iterative Method)
(Convergence, Applied Mathematics and Computational Science, Splitting, PARTIAL DIFFERENTIAL EQUATION, Parallel Algorithm, Numerical Analysis and Computational Mathematics, High Dimensionality, Parallelization, Differential equation, Fractional-step Method, Boundary Value Problem, Electrical And Electronic Engineering, Elliptic equation, and Iterative Method)
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Acceso de usuarios registrados. Acceso de usuarios registrados Usuario Contraseña. ...
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Recordamos resultados y presentamos problemas abiertos acerca de la influencia del perfil y la rugosidad de un cuerpo sólido sobre su resistencia al arrastre hidrodinámico. Mostramos además que, asintóticamente, un fluido no puede... more
Recordamos resultados y presentamos problemas abiertos acerca de la influencia del perfil y la rugosidad de un cuerpo sólido sobre su resistencia al arrastre hidrodinámico. Mostramos además que, asintóticamente, un fluido no puede deslizarse sobre una pared recubierta de asperezas minúsculas si éstas son demasiado numerosas: en tal caso, se adhiere a la pared.Dirección General de Enseñanza Superior (DGES). Españ
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Este articulo contiene un relato de los acontecimientos que han acompanado el intento de creacion del Instituto Espanol de Matematicas (IEMath), incluyendo comentarios sobre el pasado reciente y el presente de esta iniciativa.