NameCasado Díaz, Juan
DepartmentEcuaciones Diferenciales y Análisis Numérico
Knowledge areaAnálisis Matemático
Professional categoryCatedrático de Universidad
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PhD Thesis
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Study of Optimal Design Problems by the Regularity Method in Nonlinear Equations

Vásquez Varas, Donato Maximiliano; Casado Díaz, Juan; Conca Rosende, Carlos (2022)
This thesis is devoted to the study of an optimal design problem, which is the maximization of the internal energy for the ...
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Increase of mass and nonlocal effects in the homogenization of magneto-elastodynamics problems

Briane, Marc; Casado Díaz, Juan (Springer, 2021)
The paper deals with the homogenization of a magneto-elastodynamics equation satisfied by the displacement uεuε of an ...
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Semilinear problems with right-hand sides singular at u = 0 which change sign

Casado Díaz, Juan; Murat, François (Elsevier, 2021)
The present paper is devoted to the study of the existence of a solution u for a quasilinear second order differential ...
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The maximization of the p-Laplacian energy for a two-phase material

Casado Díaz, Juan; Conca Rosende, Carlos; Vásquez Varas, Donato Maximiliano (SIAM Publications Library, 2021)
We consider the optimal arrangement of two diffusion materials in a bounded openset \Omega \subset \BbbR Nin order to ...
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Numerical Maximization of the p-Laplacian Energy of a Two-Phase Material

Casado Díaz, Juan; Conca Rosende, Carlos; Vásques Varas, Donato (SIAM, 2021)
For a diffusion problem modeled by thep-Laplacian operator, we are interested inobtaining numerically the two-phase material ...
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Homogenization of an elastodynamic system with a strong magnetic field and soft inclusions inducing a viscoelastic effective behavior

Briane, Marc; Casado Díaz, Juan (Elsevier, 2020)
In this paper we study homogenization of a linear system of elastodynamics in an elastic body with soft inclusions, which ...
Final Degree Project
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Una introducción al formalismo matemático de la Mecánica Cuántica

Bernal González, Alexander; Casado Díaz, Juan (2020)
The aim of this work is to introduce the mathematical tools needed in order to explain, in a more rigorous way, the basic ...
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On existence of optimal potentials on unbounded domains

Buttazzo, Giuseppe; Casado Díaz, Juan; Maestre, Faustino (Cornell University, 2019)
We consider elliptic equations of Schrödinger type with a right-hand side fixed and with the linear part of order zero ...
Final Degree Project
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Teoría del grado y aplicación a la resolución de ecuaciones diferenciales

Zambrano Monge, Esperanza María; Casado Díaz, Juan (2018)
El objetivo de la presente memoria es introducir los elementos básicos de la teoría del grado en espacios de dimensión ...
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A new algorithm of proper generalized decomposition for parametric symmetric elliptic problems

Azaïez, Majdi; Ben Belgacem, Faker; Casado Díaz, Juan; Chacón Rebollo, Tomás; Murat, François (Society for Industrial and Applied Mathematics, 2018)
We introduce a new algorithm of proper generalized decomposition (PGD) for parametric symmetric elliptic partial differential ...
Final Degree Project
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Introducción a la optimización infinito dimensional

Peña Gallardo, Miguel; Casado Díaz, Juan; Luna Laynez, Manuel (2017)
El objetivo de este trabajo es obtener un resultado general acerca de la existencia de solución de problemas de minimización ...
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Γ-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients

Briane, Marc; Casado Díaz, Juan; Luna Laynez, Manuel; Pallares Martín, Antonio Jesús (Elsevier, 2017)
The present paper deals with the asymptotic behavior of equi-coercive sequences {Fn} of nonlinear functionals defined over ...
PhD Thesis
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Problemas de homogeneización con alto contraste

Pallares Martín, Antonio Jesús; Casado Díaz, Juan; Luna Laynez, Manuel (2016)
El objetivo de esta tesis es estudiar la homogeneización de sistemas de ecuaciones en derivadas parciales elípticas. ...
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A characterization result for the existence of a two-phase material minimizing the first eigenvalue

Casado Díaz, Juan (Elsevier, 2016)
Given two isotropic homogeneous materials represented by two constants 0 <α< | |, we consider here the problem consisting ...
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A new div-curl result. Applications to the homogenization of elliptic systems and to the weak continuity of the Jacobian

Briane, Marc; Casado Díaz, Juan (Elsevier, 2016)
In this paper a new div-curl result is established in an open set Ω of R N , N ≥ 2, for the product of two sequences of ...
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Smoothness properties for the optimal mixture of two isotropic materials the compliance and eigenvalue problems

Casado Díaz, Juan (Society for Industrial and Applied Mathematics, 2015)
The present paper is devoted to obtaining some smoothness results for the solution of two classical control problems ...
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A corrector for a wave problem with periodic coefficients in a 1D bounded domain

Casado Díaz, Juan; Couce Calvo, Julio; Maestre Caballero, Faustino; Martín Gómez, José Domingo (EDP Sciences, 2015)
We consider a wave problem posed in a bounded open interval of R, where the coefficients, the initial conditions and the ...
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The behavior of a beam fixed on small sets of one of its extremities

Casado Díaz, Juan; Luna Laynez, Manuel; Murat, François (AIMS, 2014)
In this paper we study the asymptotic behavior of the solution of an anisotropic, heterogeneous, linearized elasticity ...
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Homogenization of systems with equi-integrable coefficients

Briane, Marc; Casado Díaz, Juan (EDP Sciences, 2014)
In this paper we prove a H-convergence type result for the homogenization of systems the coefficients of which satisfy a ...
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Homogenization of convex functionals which are weakly coercive and not equi-bounded from above

Briane, Marc; Casado Díaz, Juan (Elsevier, 2013)
This paper deals with the homogenization of nonlinear convex energies defined in W_{0}^{1,1}(\Omega )W01,1(Ω), for a regular ...
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Homogenization and correctors for monotone problems in cylinders of small diameter

Casado Díaz, Juan; Murat, François; Sili, Ali (Elsevier, 2013)
In this paper we study the homogenization of monotone diffusion equations posed in an N-dimensional cylinder which converges ...
Presentation
Presentation
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Homogenization of the Poisson equation with Dirichlet conditions in random perforated domains

Calvo Jurado, Carmen; Casado Díaz, Juan; Luna Laynez, Manuel; Hamilton, I.P.; Vigo Aguiar, Jesús (Computational and Mathematical Methods in Science and Engineering, 2013)
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Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary

Casado Díaz, Juan; Luna Laynez, Manuel; Suárez Grau, Francisco Javier (Society for Industrial and Applied Mathematics, 2013)
We study the asymptotic behavior of the solutions of the Navier–Stokes system in a thin domain Ωε of thickness ε satisfying ...
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Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations

Briane, Marc; Casado Díaz, Juan (Springer, 2012)
The paper deals with the homogenization of rigid heterogeneous plates. Assuming that the coefficients are equi-bounded in ...
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On the Navier boundary condition for viscous fluids in rough domains

Casado Díaz, Juan; Luna Laynez, Manuel; Suárez Grau, Francisco Javier (Sociedad Española de Matemática Aplicada, 2012)
In this paper we review some recent results concerning the study of the asymptotic behavior of viscous fluids in rough ...
PhD Thesis
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Comportamiento asintótico de fluidos viscosos con condiciones de deslizamiento sobre fronteras rugosas

Suárez Grau, Francisco Javier; Luna Laynez, Manuel; Casado Díaz, Juan (2011)
Un problema importante en mecánica de fluidos consiste en la elección adecuada de las condiciones de frontera. Una hipótesis ...
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Homogenization and corrector for the wave equation with discontinuous coefficients in time

Casado Díaz, Juan; Couce Calvo, Julio; Maestre, Faustino; Martín Gómez, José Domingo (Elsevier, 2011)
In this paper we analyze the homogenization of the wave equation with bounded variation coefficients in time, generalizing ...
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Estimate of the pressure when its gradient is the divergence of a measure. Applications

Briane, Marc; Casado Díaz, Juan (EDP Sciences, 2011)
In this paper, a W−1,N estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure ...
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Numerical approximation of a one-dimensional elliptic optimal design problem

Casado Díaz, Juan; Castro Barbero, Carlos Manuel; Luna Laynez, Manuel; Zuazua Iriondo, Enrique (Society for Industrial and Applied Mathematics, 2011)
We address the numerical approximation by finite-element methods of an optimal design problem for a two phase material in ...
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A viscous fluid in a thin domain satisfying the slip condition on a slightly rough boundary

Casado Díaz, Juan; Luna Laynez, Manuel; Suárez Grau, Francisco Javier (ScienceDirect, 2010)
We consider a viscous fluid of small height ε on a periodic rough bottom Γε of period rε and amplitude δε, δε rε ε, where ...
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A viscous fluid in a thin domain satisfying the slip condition on a slightly rough boundary

Casado Díaz, Juan; Luna Laynez, Manuel; Suárez Grau, Francisco Javier (Elsevier, 2010)
We consider a viscous fluid of small height ε on a periodic rough bottom Γε of period rε and amplitude δε, δε rε ε, where ...
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The div-curl lemma “trente ans après”: an extension and an application to the G-convergence of unbounded monotone operators

Briane, Marc; Casado Díaz, Juan; Murat, François (Elsevier, 2009)
In this paper new div-curl results are derived. For any open set Ω of RN, N⩾2, we study the limit of the product vn⋅wn ...
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Homogenization of non-uniformly bounded periodic diffusion energies in dimension two

Braides, Andrea; Briane, Marc; Casado Díaz, Juan (IOP Publishing, 2009)
This paper deals with the homogenization of two-dimensional oscillating convex functionals, the densities of which are ...
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Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets

Calvo Jurado, Carmen; Casado Díaz, Juan; Luna Laynez, Manuel (EDP Sciences, 2009)
For a fixed bounded open set Ω ⊂ RN , a sequence of open sets Ωn ⊂ Ω and a sequence of sets Γn ⊂ ∂Ω ∩ ∂Ωn, we study the ...
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Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients

Briane, Marc; Casado Díaz, Juan (Elsevier, 2008)
This paper deals with the behavior of two-dimensional linear elliptic equations with unbounded (and possibly infinite) ...
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Relaxation of a control problem in the coefficients with a functional of quadratic growth in the gradient

Casado Díaz, Juan; Couce Calvo, Julio; Martín Gómez, José Domingo (Society for Industrial and Applied Mathematics, 2008)
We study an optimal design problem consisting in mixing two anisotropic (electric or thermal) materials in order to minimize ...
Presentation
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Relajación de problemas de control en los coeficientes con un funcional dependiendo del gradiente

Casado Díaz, Juan; Couce Calvo, Julio; Martín Gómez, José Domingo (2007)
Se considera un problema de diseño ´optimo consistente en mezclar dos materiales (eléctricos o térmicos) anisótropos de ...
Presentation
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Comportamiento asintótico de una viga elástica fijada en pequeñas zonas de uno de sus extremos

Casado Díaz, Juan; Luna Laynez, Manuel; Murat, François (2007)
Estudiamos el comportamiento asintótico de una viga elástica delgada cuando su anchura, ε, tiende a cero. La viga está ...
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Asymptotic behaviour of equicoercive diffusion energies in dimension two

Briane, Marc; Casado Díaz, Juan (Springer, 2007)
In this paper, we study the asymptotic behaviour of a given equicoercive sequence of diffusion energies Fn, n ∈ N, defined ...
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Nonlocal limits in the study of linear elliptic systems arising in periodic homogenization

Calvo Jurado, Carmen; Casado Díaz, Juan (Elsevier, 2007)
In the present paper, we obtain the two-scale limit system of a sequence of linear elliptic periodic problems with varying ...
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Two-Dimensional Div-Curl Results: Application to the Lack of Nonlocal Effects in Homogenization

Briane, Marc; Casado Díaz, Juan (Taylor & Francis, 2007)
In this paper, we study the asymptotic behaviour of sequences of conduction problems and sequences of the associated ...
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Uniqueness results for pseudomonotone problems with p>2

Casado Díaz, Juan; Murat, François; Porretta, Alessio (French Academy of Sciences, 2007)
We consider a pseudomonotone operator, the model of which is −div(b(x, u)|∇ u| p−2∇ u) with 1 <p< +∞ and b(x, s) a Lipschitz ...
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Finite elements approximation of second order linear elliptic equations in divergence formwith right-hand side in L1

Casado Díaz, Juan; Chacón Rebollo, Tomás; Girault, Vivette; Gómez Mármol, María Macarena; Murat, François (Springer, 2007)
In this paper we consider, in dimension d≥ 2, the standard P1P1 finite elements approximation of the second order linear ...
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Homogenization of Dirichlet parabolic problems for coefficients and open sets simultaneously variable and applications to optimal design

Calvo Jurado, Carmen; Casado Díaz, Juan (Elsevier, 2006)
In a previous paper, we studied the homogenization of a sequence of parabolic linear Dirichlet problems, when the coefficients ...
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Exponential decay for the solutions of nonlinear elliptic systems posed in unbounded cylinders☆

Casado Díaz, Juan (Elsevier, 2006)
We study the asymptotic behavior at infinity of the solutions of a nonlinear elliptic system posed in a cylinder of infinite ...
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A density result for the variation of a material with respect to small inclusions

Casado Díaz, Juan; Couce Calvo, Julio; Martín Gómez, José Domingo (Elsevier, 2006)
We consider the family of materials obtained, via homogenization, by replacing a small portion, of size ɛ, of a fixed ...
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A density result for the variation of a material with respect to small inclusions

Casado Díaz, Juan; Couce Calvo, Julio; Martín Gómez, José Domingo (Elsevier, 2006)
We consider the family of materials obtained, via homogenization, by replacing a small portion, of size ɛ, of a fixed ...
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Homogenization of very thin elastic reticulated structures

Casado Díaz, Juan; Luna Laynez, Manuel; Martín Gómez, José Domingo (De Gruyter, 2005)
This work is devoted to the homogenization of the anisotropic, linearized elasticity system posed on thin reticulated ...
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Asymptotic behaviour of linear Dirichlet parabolic problems with variable operators depending on time in varying domains

Calvo Jurado, Carmen; Casado Díaz, Juan (Elsevier, 2005)
We study the asymptotic behaviour of the solutions of linear parabolic Dirichlet problems when the coefficients and the ...
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Lack of compactness in two-scale convergence

Briane, Marc; Casado Díaz, Juan (Society for Industrial and Applied Mathematics, 2005)
This article deals with the links between compensated compactness and two-scale convergence. More precisely, we ask the ...
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Asymptotic behavior of an elastic beam fixed on a small part of one of its extremities

Casado Díaz, Juan; Luna Laynez, Manuel; Murat, François (Elsevier, 2004)
We study the asymptotic behavior of the solution of an anisotropic, heterogeneous, linearized elasticity problem in a ...
Article
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Asymptotic behavior of diffusion problems in a domain made of two cylinders of different diameters and lengths

Casado Díaz, Juan; Luna Laynez, Manuel; Murat, François (Elsevier, 2004)
We study the asymptotic behavior of the solution of a diffusion problem posed in the union of a cylinder of small diameter and ...
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Optimality conditions for nonconvex multistate control problems in the coefficients

Casado Díaz, Juan; Couce Calvo, Julio; Martín Gómez, José Domingo (Society for Industrial and Applied Mathematics, 2004)
The purpose of this paper is to attain some optimality conditions for the identification of a diffusion matrix (material) ...
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Why viscous fluids adhere to rugose walls

Casado Díaz, Juan; Fernández Cara, Enrique; Simon, Jacques (Elsevier, 2003)
The main purpose of this paper is to justify rigorously the following assertion: A viscous fluid cannot slip on a wall ...
Chapter of Book
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Numerical solution of a Laplace equation with data in L1

Casado Díaz, Juan; Chacón Rebollo, Tomás; Gómez Mármol, María Macarena; Girault, Vivette; Murat, François; Palacios Latasa, Manuel Pedro; Trujillo, David; Torrens Iñigo, Juan José; Madaune-Tort, Monique; López de Silanes Busto, María Cruz; Sanz Sáiz, Gerardo (Universidad de Zaragoza, 2003)
In this work, we address the numerical solution of the Laplace equation with data in L1 by IP1 finite element schemes. ...
PhD Thesis
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Homogeneización de problemas de Dirichlet para dominios y coeficientes simultáneamente variables

Calvo Jurado, Carmen; Casado Díaz, Juan (2003)
En esta memoria se estudia el comportamiento asintótico de las soluciones de ecuaciones en derivadas parciales de tipo ...
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Results on existence of solution for an optimal design problem

Calvo Jurado, Carmen; Casado Díaz, Juan (Universidad de Extremadura, 2003)
In this paper we study a control problem for elliptic nonlinear monotone problems with Dirichlet boundary conditions where ...
PhD Thesis
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Homogeneización de estructuras reticuladas: un método multiescala

Luna Laynez, Manuel; Casado Díaz, Juan; Martín Gómez, José Domingo (2003)
En la Memoria se introduce un nuevo método para estudiar el comportamiento asintótico de las soluciones de problemas en ...
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The two-scale convergence method applied to generalized Besicovitch spaces

Casado Díaz, Juan; Gayte Delgado, María Inmaculada (The Royal Society, 2002)
The two-scale convergence method has proved to be a very useful tool for dealing with periodic homogenization problems. ...
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Why viscous fluids adhere to rugose walls: A mathematical explanation

Casado Díaz, Juan; Fernández Cara, Enrique; Simon, Jacques (ScienceDirect, 2002)
The main purpose of this paper is to justify rigorously the following assertion: A viscous fluid cannot slip on a wall ...
Article
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The limit of Dirichlet systems for variable monotone operators in general perforated domains

Calvo Jurado, Carmen; Casado Díaz, Juan (Elsevier, 2001)
We study the asymptotic behaviour of the solutions of nonlinear Dirichlet systems when the operators and the open sets ...
Presentation
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Efecto de la rugosidad en el deslizamiento de un fluido sobre una pared

Simon, Jacques; Casado Díaz, Juan; Fernández Cara, Enrique (2001)
Recordamos resultados y presentamos problemas abiertos acerca de la influencia del perfil y la rugosidad de un cuerpo ...
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Algunos trabajos relacionados con la teoría de E.D.P. y su homogeneización

Casado Díaz, Juan (Sociedad Española de Matemática Aplicada, 2000)
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Asymptotic behavior of nonlinear elliptic systems on varying domains

Casado Díaz, Juan; Garroni, Adriana (Society for Industrial and Applied Mathematics, 2000)
We consider a monotone operator of the form Au = −div(a(x, Du)), with Ω ⊆ Rn and a : Ω×MM×N → MM×N , acting on W1,p 0 (Ω, ...
PhD Thesis
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Espacios de Besicovitch generalizados y convergencia en dos escalas

Gayte Delgado, María Inmaculada; Casado Díaz, Juan; Couce Calvo, Julio (1998)
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Homogenization of general quasi-linear Dirichlet problems with quadratic growth in perforated domains

Casado Díaz, Juan (Elsevier, 1997)
In this paper, we study the homogenization of a Dirichlet problem in perforated domains for an operator which is the ...
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Homogenization of a quasi-linear problem with quadratic growth in perforated domains: An example

Casado Díaz, Juan (Elsevier, 1997)
We study the homogenization of Dirichlet problems for a fixed quasi-linear operator which is the perturbation of the Laplace ...
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Existence of a sequence satisfying Cioranescu-Murat conditions in homogenization of Dirichlet problems in perforated domains

Casado Díaz, Juan (Sapienza Università di Roma, 1996)
In a paper of 1982, D. Cioranescu and F. Murat considered the problem satisfied by the limit u of the sequence un solution ...
PhD Thesis
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Sobre la homogeneización de problemas no coercivos y problemas en dominios con agujeros

Casado Díaz, Juan; Murat, François; Martín Gómez, José Domingo (1993)
En esta memoria se estudian dos problemas. El primero hace referencia a la relajación de un funcional energía sobre el ...