18 citations · 96 across the 20 of their papers we have counts for
22 papers
Characterizing the breakdown of the maximum principle in a class of nonlocal elliptic problems
João R. Santos Júnior, Silvia Sastre-Gómez, Diego A. Souza
In this paper, we consider a nonlocal elliptic equation involving a nonnegative parameter that quantifies the strength of the nonlocal term, posed in a smooth bounded domain wi…
Optimal cost for the null controllability of the Stokes system with controls having components and applications
Felipe W. Chaves-Silva, Marcos G. Ferreira-Silva, Diego A. Souza
In this work, we investigate the optimal cost of null controllability for the -dimensional Stokes system when the control acts on scalar components. We establish a novel s…
Numerical null controllability of parabolic PDEs using Lagrangian methods
Enrique Fernandez-Cara, Roberto Morales, Diego A. Souza
In this paper, we study several theoretical and numerical questions concerning the null controllability problems for linear parabolic equations and systems for several dimensions.…
A mixed formulation for the direct approximation of -weighted controls for the linear heat equation
Arnaud Münch, Diego A. Souza
This paper deals with the numerical computation of null controls for the linear heat equation. The goal is to compute approximations of controls that drive the solution from a pres…
Remarks on the control of two-phase Stefan free-boundary problems
Raul K. C. Araújo, Enrique Fernández-Cara, Juan Límaco +1
This paper concerns the null controllability of the two-phase 1D Stefan problem with distributed controls. This is a free-boundary problem that models solidification or melting pro…
Boundary controllability of incompressible Euler fluids with Boussinesq heat effects
Enrique Fernández-Cara, Maurício C. Santos, Diego A. Souza
This paper deals with the boundary controllability of inviscid incompressible fluids for which thermal effects are important. They will be modeled through the so called Boussinesq…
On the numerical controllability of the two-dimensional heat, Stokes and Navier-Stokes equations
Enrique Fernández-Cara, Arnaud Münch, Diego A. Souza
The aim of this work is to present some strategies to solve numerically controllability problems for the two-dimensional heat equation, the Stokes equations and the Navier-Stokes e…
Uniform local null control of the Leray- model
Fágner D. Araruna, Enrique Fernández-Cara, Diego A. Souza
This paper deals with the distributed and boundary controllability of the so called Leray- model. This is a regularized variant of the Navier-Stokes system ( is a small posit…
On the control of the Burgers-alpha model
Fágner D. Araruna, Enrique Fernández-Cara, Diego A. Souza
This work is devoted to prove the local null controllability of the Burgers- model. The state is the solution to a regularized Burgers equation, where the transport term is of t…
On the control of some coupled systems of the Boussinesq kind with few controls
Enrique Fernández-Cara, Diego A. Souza
This paper is devoted to prove the local exact controllability to the trajectories for a coupled system, of the Boussinesq kind, with a reduced number of controls. In the state sys…
Quantitative unique continuation for real-valued solutions to second order elliptic equations in the plane
Kévin Le Balc'h, Diego A. Souza
In this article, we study a quantitative form of the Landis conjecture on exponential decay for real-valued solutions to second order elliptic equations with variable coefficients…
Remarks on the controllability of parabolic systems with non-diagonalizable diffusion matrix
Michel Duprez, Manuel González-Burgos, Diego A. Souza
The distributed null controllability for coupled parabolic systems with non-diagonalizable diffusion matrices with a reduced number of controls has been studied in the case of cons…
Exact controllability to the trajectories of the one-phase Stefan problem
Jon Asier Bárcena-Petisco, Enrique Fernández-Cara, Diego A. Souza
This paper deals with the exact controllability to the trajectories of the one--phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidific…
Switching Controls for Analytic Semigroups and Applications to Parabolic Systems
Felipe W. Chaves-Silva, Sylvain Ervedoza, Diego A. Souza
In this work, we push further the analysis of the problem of switching controls proposed in [E. Zuazua, Switching control, J. Eur. Math. Soc. (JEMS), 13(1): 85--117, 2011]. The pro…
On the Uniform Controllability of the Inviscid and Viscous Burgers- Systems
Raul K. C. Araújo, Enrique Fernández-Cara, Diego A. Souza
This work is devoted to prove the global uniform exact controllability of the inviscid and viscous Burgers- systems. The state is the solution to a regularized Burgers equat…
Small-time global exact controllability to the trajectories for the viscous Boussinesq system
F. W. Chaves-Silva, E. Fernández-Cara, K. Le Balc'h +2
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 f…
On Some Geometric Inverse Problems for Nonscalar Elliptic Systems
Raul K. C. Araújo, Enrique Fernández-Cara, Diego A. Souza
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observ…
Non null controllability of Stokes equations with memory
Enrique Fernández-Cara, José Lucas F. Machado, Diego A. Souza
In this paper, we study the null controllability of the three-dimensional Stokes equations with a memory term. For any positive final time , we construct initial conditions su…
On the controllability of some equations of Sobolev-Galpern type
F. W. Chaves-Silva, Diego A. Souza
In this paper we deal with the controllability problem for some Sobolev type equations. We show that the equations cannot be driven to zero if the control region is strictly suppor…
Observability inequalities on measurable sets for the Stokes system and applications
Felipe W. Chaves-Silva, Diego A. Souza, Can Zhang
In this paper, we establish spectral inequalities on measurable sets of positive Lebesgue measure for the Stokes operator, as well as an observability inequalities on space-time me…
On the One-Dimensional Nonlinear Monodomain Equations with Moving Controls
Karl Kunisch, Diego A. Souza
In this paper local exact controllability to the trajectories for the one-dimensional monodomain equations with the FitzHugh-Nagumo and Rogers-McCulloch ionic models using distribu…
Inverse problems for linear parabolic equations using mixed formulations - Part 1 : Theoretical analysis
Arnaud Munch, Diego Souza
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solutio…