On a class of non-linear parabolic control systems with memory effects

Abstract

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 and with homogeneous Dirichlet boundary conditions. The control is assumed to be distributed along a subdomain ω of Ω. 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.