Work

Controllability of some semilinear shadow reaction-diffusion systems

Year: 2024

Type: article

Abstract: The shadow limit is a versatile tool used to study the reduction of reaction-diffusion systems into simpler PDE-ODE models by letting one of the diffusion coefficients tend to infinity. This reduction has been used to understand different qualitative properties and their interplay between the original model and its reduced version. The aim of this work is to extend previous results about the controllability of linear reaction-diffusion equations and how this property is inherited by the corresponding shadow model. Defining a suitable class of nonlinearities and improving some uniform Carleman estimates, we extend the results to the semilinear case and prove that the original model is null-controllable and that the shadow limit preserves this important feature.

Source: Asymptotic Analysis

DOI: 10.3233/asy-241930

Authors: Víctor Hernández-Santamaría, Alberto Peña-García

Institution: Universidad Nacional Autónoma de México

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Institut national de recherche en informatique et en automatique (INRIA), Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México

Awards: G2005782840, G2865518804