Interior Controllability of a Broad Class of Reaction Diffusion Equations

Hugo Leiva and Yamilet Quintana

Mathematical Problems in Engineering, 2009, vol. 2009, 1-8

Abstract:

We prove the interior approximate controllability of the following broad class of reaction diffusion equation in the Hilbert spaces given by , , where is a domain in , is an open nonempty subset of , denotes the characteristic function of the set , the distributed control and is an unbounded linear operator with the following spectral decomposition: . The eigenvalues of have finite multiplicity equal to the dimension of the corresponding eigenspace, and is a complete orthonormal set of eigenvectors of . The operator generates a strongly continuous semigroup given by . Our result can be applied to the D heat equation, the Ornstein-Uhlenbeck equation, the Laguerre equation, and the Jacobi equation.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:708516

DOI: 10.1155/2009/708516

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