Table of Contents
International Journal of Partial Differential Equations
Volume 2013 (2013), Article ID 424309, 7 pages
http://dx.doi.org/10.1155/2013/424309
Research Article

Approximate Controllability of a Semilinear Heat Equation

1Universidad de Los Andes, Facultad de Ciencias, Departamento de Matemática, Mérida 5101, Venezuela
2Universidad Central de Venezuela, Facultad de Ciencias, Departamento de Matemática, Caracas 1051, Venezuela

Received 8 April 2013; Accepted 11 September 2013

Academic Editor: Michael Grinfeld

Copyright © 2013 Hugo Leiva et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We apply Rothe’s type fixed point theorem to prove the interior approximate controllability of the following semilinear heat equation: in on , where is a bounded domain in , , is an open nonempty subset of , denotes the characteristic function of the set , the distributed control belongs to , and the nonlinear function is smooth enough, and there are , and such that for all Under this condition, we prove the following statement: for all open nonempty subset of , the system is approximately controllable on . Moreover, we could exhibit a sequence of controls steering the nonlinear system from an initial state to an neighborhood of the final state at time .