Interior controllability of a broad class of reaction diffusion equations. (English) Zbl 1206.93017
Summary: 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.
|80A20||Heat and mass transfer, heat flow|