Approximate controllability of semilinear reaction diffusionequations

Hugo Leiva; Nelson Merentes; José L. Sánchez

doi:10.3934/mcrf.2012.2.171

Article Contents

2012, Volume 2, Issue 2: 171-182. Doi: 10.3934/mcrf.2012.2.171

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Approximate controllability of semilinear reaction diffusion equations

1.
Universidad de los Andes, Facultad de Ciencias, Departamento de Matemática, Mérida 5101
2.
Universidad Central de Venezuela, Facultad de Ciencias, Departamento de Matemática, Caracas 1051
3.
Universidad Central de Venezuela, Facultad de Ciencias, Departamento de Matem, Caracas 1051

Received: October 31, 2011

Revised: December 31, 2011

Published: May 2012

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Abstract

In this paper we prove the approximate controllability of the a broad class of semilinear reaction diffusion equation in a Hilbert space, with application to the semilinear $n$D heat equation, the Ornstein-Uhlenbeck equation, amount others.

Keywords:

Interior controllability,
semilinear reaction diffusion equations,
strongly continuous semigroups,
heat equation,
compact semigroups.

Mathematics Subject Classification: Primary: 93B05; Secondary: 93C10.

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