Interior Controllability of a
Reaction-Diffusion System with Cross-Diffusion Matrix !()
Departamento de Matemáticas, Universidad de Los Andes, Mérida 5101, Venezuela
Boundary Value Problems 2009, 2009:560407 doi:10.1155/2009/560407Published: 11 June 2009
We prove the interior approximate controllability for the following reaction-diffusion system with cross-diffusion matrix in , in , , on , , , , where is a bounded domain in , , the diffusion matrix has semisimple and positive eigenvalues , is an arbitrary constant, is an open nonempty subset of , denotes the characteristic function of the set , and the distributed controls . Specifically, we prove the following statement: if (where is the first eigenvalue of ), then for all and all open nonempty subset of the system is approximately controllable on .