International Journal of applied mathematics and computer science

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Paper details

Number 4 - December 1999
Volume 9 - 1999

Approximate controllability properties of the semilinear heat equation with lumped controls

Alexander Yu Khapalov

In this article, we study the global controllability properties of a one-dimensional semilinear heat equation with sublinear reaction term, governed in a bounded domain by internal lumped controls. We prove that it is possible to exactly control any finite dimensional portion of its solution (when expanded along the sequence of the eigenfunctions of the associated Laplacian), provided that the truncated linear equation is approximately controllable in L2(0,1). We also describe a certain topology (weaker than L2(0,1)) in which this system is, in fact, globally approximately controllable at any positive time. Some extensions to the case of several dimensions are also given.

semilinear heat equation, controllability, internal lumped control