2007 Some results on controllability for linear and nonlinear heat equations in unbounded domains
Manuel González-Burgos, Luz de Teresa
Adv. Differential Equations 12(11): 1201-1240 (2007). DOI: 10.57262/ade/1355867413

Abstract

In this paper we present some results concerning the null controllability for a heat equation in unbounded domains. We characterize the conditions that must satisfy the auxiliary function that leads to a global Carleman inequality for the adjoint problem and then to get a null controllability result. We give some examples of unbounded domains $(\Omega,\omega)$ that satisfy these sufficient conditions. Finally, when $\Omega\setminus \overline \omega$ is bounded, we prove the null controllability of the semilinear heat equation when the nonlinearity $f(y,\nabla y)$ grows more slowly than $|y|\log^{3/2}(1+|y|+|\nabla y|)+ |\nabla y|\log^{1/2}(1+|y|+|\nabla y|)$ at infinity (generally in this case in the absence of control, blow-up occurs). In this aim we also prove the linear null controllability problem with $L^\infty$-controls.

Citation

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Manuel González-Burgos. Luz de Teresa. "Some results on controllability for linear and nonlinear heat equations in unbounded domains." Adv. Differential Equations 12 (11) 1201 - 1240, 2007. https://doi.org/10.57262/ade/1355867413

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1170.93007
MathSciNet: MR2372238
Digital Object Identifier: 10.57262/ade/1355867413

Subjects:
Primary: 93B05
Secondary: 35K20 , 93B07 , 93C20

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.12 • No. 11 • 2007
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