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Artículo
On the Navier boundary condition for viscous fluids in rough domains
(Sociedad Española de Matemática Aplicada, 2012-04)
In this paper we review some recent results concerning the study of the asymptotic behavior of viscous fluids in rough domains assuming Navier boundary conditions on the rough boundary. Our main interest is to study the ...
Artículo
Smoothness properties for the optimal mixture of two isotropic materials the compliance and eigenvalue problems
(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 relative to the optimal mixture of two isotropic materials. In the first one, the goal is to maximize the ...
Artículo
Optimality conditions for nonconvex multistate control problems in the coefficients
(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) under several restrictions. Assuming that the set of such diffusion matrices is closed for the ...
Artículo
Numerical approximation of a one-dimensional elliptic optimal design problem
(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 one space dimension. This problem, in the continuous setting, due to high frequency oscillations, ...
Artículo
Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
(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 the Navier boundary condition on a periodic rough set Γε ⊂ ∂Ωε of period rε and amplitude δε, with ...
Artículo
Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets
(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 asymptotic behavior of the solution of a nonlinear elliptic system posed on Ωn, satisfying Neumann ...
Artículo
Relaxation of a control problem in the coefficients with a functional of quadratic growth in the gradient
(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 a functional depending on the gradient of the state. It is known that this type of problem has ...