Laboratoire LAIG, Université du 08 Mai 1945, BP. 401, Guelma 24000, Algeria
Copyright © 2010 Salah Badraoui. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the following reaction-diffusion system with a cross-diffusion matrix and fractional derivatives
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 .