Research Article
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:10.1155/2010/281238
Published: 19 January 2010Abstract
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 
.
