Null controllability in unbounded domains for the semilinear heat equation with nonlinearities involving gradient terms
type: Item
instance of: scholarly article
title: Null controllability in unbounded domains for the semilinear heat equation with nonlinearities involving gradient terms
zbMATH Open document ID: 0997.93048
DOI: 10.1023/A:1017515027783
author: Enrique Zuazua
author: Victor R. Cabanillas
author: Silvano B. de Menezes
published in: Journal of Optimization Theory and Applications
publication date: 2002-08-12T00:00:00Z
review text: \noindent The system is described by the parabolic equation \[ \begin{align*}{ {\partial y(t, x) \over \partial t} &= \Delta y(t, x) - f(y(t, x), \nabla y(t, x)) + u(t, x) \chi_\omega(x) \quad (t \ge 0, x \in \Omega) , \cr y(t, x) &= 0 \quad (t \ge 0, x \in \Gamma) , \qquad u(0, x) = u_0(x) \quad (x \in \Omega) }\end{align*} \] in an unbounded \(n\)-dimensional domain \(\Omega\) with boundary \(\Gamma;\) \(\chi_\omega(x)\) is the characteristic function of a subdomain \(\omega \subset \Omega\) and \(u(\cdot, \cdot) \in L^2((0, T) \times \Omega)\) is the control. The nonlinearity satisfies \(f(0, 0) = 0.\) The authors show that, if \(\Omega \setminus \omega\) is bounded, the system is null controllable under suitable smoothness assumptions.
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 1779063
zbMATH Keywords: null controllability
zbMATH Keywords: heat equation
zbMATH Keywords: distributed parameter systems
reviewed by: Hector O. Fattorini
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1779063