arXiv subjects

Miguel R. Nuñez-Chávez

Publications and source records attributed to Miguel R. Nuñez-Chávez.

3 recordsLinked to original sources

arXiv2025

Existence, Stability and Controllability of the parabolic-parabolic thermistor model

In this article we establish the well-posedness, energy estimates, stability, and local null controllability for the thermistor system modeled by a parabolic-parabolic system using a control force acting on just one equation of the system. The proof of the controllability is based on appropriate Carleman estimates and Liusternik's inverse function theorem to obtain the local controllability of the nonlinear system. The coupling of the system happens both in the terms of order zero and one, which requires the use of a special Carleman estimate for the system.

math.AP↗

arXiv2025

Insensitizing controls for a quasi-linear parabolic equation with diffusion depending on gradient of the state

In this paper, a quasi-linear parabolic equation with a diffusion term dependent on the gradient to the state with Dirichlet boundary conditions is considered. The goal of this paper is to prove the existence of control that insensitizes the system under study which is the case that Xu Liu left open in 2012. It is well known that the insensitizing control problem is equivalent to a null controllability result for a cascade system, which is obtained by duality arguments, Carleman estimates, and the Right Inverse mapping theorem. Also, some possible extensions and open problems concerning other quasi-linear systems are presented.

math.AP↗

arXiv2021

Controllability Under Positive Constraints for Quasilinear Parabolic PDEs

This paper deals with the analysis of the internal control with constraint of positive kind of a parabolic PDE with nonlinear diffusion when the time horizon is large enough. The minimal controllability time will be strictly positive. We prove a global steady state constrained controllability result for a quasilinear parabolic with nonlinearity in the diffusion term. Then, under suitable dissipative assumption in the system and local controllability results, we conclude the result to any initial datum and any target trajectory.

math.AP↗