Research Article
Interior Controllability of a ![]()
Departamento de Matemáticas, Universidad de Los Andes, Mérida 5101, Venezuela
Boundary Value Problems 2009, 2009:560407 doi:10.1155/2009/560407
Published: 11 June 2009Abstract
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 
.
