Approximate Controllability of a Reaction-Diffusion System with a Cross-Diffusion Matrix and Fractional Derivatives on Bounded Domains
Laboratoire LAIG, Université du 08 Mai 1945, BP. 401, Guelma 24000, Algeria
Boundary Value Problems 2010, 2010:281238 doi:10.1155/2010/281238Published: 19 January 2010
We study the following reaction-diffusion system with a cross-diffusion matrix and fractional derivatives in , in , on , , in where is a smooth bounded domain, , the diffusion matrix has semisimple and positive eigenvalues , , is an open nonempty set, and is the characteristic function of . Specifically, we prove that under some conditions over the coefficients , the semigroup generated by the linear operator of the system is exponentially stable, and under other conditions we prove that for all the system is approximately controllable on .