Local exact controllability of a reaction-diffusion system
type: Item
instance of: scholarly article
title: Local exact controllability of a reaction-diffusion system
zbMATH Open document ID: 1013.93028
author: Sebastian Aniţa
author: Viorel Barbu
published in: Differential and Integral Equations
publication date: 2003-06-19T00:00:00Z
review text: The system consists of the two coupled parabolic equations \[ \begin{aligned} {\partial y(t, x) \over \partial t} &- k_1 \Delta y(t, x) + \alpha a(x) y(t, x) z(t, x) = f(x) + u(t, x),\\ {\partial z(t, x) \over \partial t} &- k_2 \Delta z(t, x) + \beta a(x) y(t, x) z(t, x) = g(x) + v(t, x) \end{aligned} \] in a bounded \(n\)-dimensional domain \(\Omega,\) \((n = 1, 2, 3)\) with Neumann boundary condition; the control functions \(u(t, x),\) \(v(t, x)\) have support \(\subseteq \omega \subset \Omega.\) Under suitable assumptions, the authors show that the system is locally null controllable. The tools are Carleman estimates for the backwards adjoint linearized system and the Schauder-Kakutani fixed point theorem.
reviewed by: Hector O. Fattorini
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 1832832
zbMATH Keywords: local controllability
zbMATH Keywords: distributed parameter systems
zbMATH Keywords: Carleman estimates
zbMATH Keywords: coupled parabolic equations
MaRDI profile type: Publication
Recommended article: Exact local controllability of a one-control reaction-diffusion system
Recommended article: Local controllability of reaction-diffusion systems around nonnegative stationary states
Recommended article: Local exact controllability of the diffusion equation in one dimension
Recommended article: Q3732096
Recommended article: Approximate controllability of a reaction-diffusion system
Recommended article: Exact controllability for a thermodiffusion system with locally distributed controls
Recommended article: Q6162694
Recommended article: Exact control of a system of diffusion equations
Recommended article: Exact controllability of nonlinear diffusion equations arising in reactor dynamics
description: scientific article; zbMATH DE number 1832832