International Journal of Control, Vol.81, No.5, 764-777, 2008
On a class of non-linear parabolic control systems with memory effects
This work establishes the local exact null controllability of non-linear parabolic integrodifferential equations with non-linearities under the integral sign in a bounded domain Omega subset of R-n and with homogeneous Dirichlet boundary conditions. The control is assumed to be distributed along a subdomain omega of Omega. Using a Carleman type inequality we first prove the global exact null controllability of a linearized equation. Then, by a fixed point method, we obtain the main result for the non-linear case. This result asserts that, when the non-linearity is of class C-1 and globally Lipschitz, the system is null controllable.