Insensitizing controls for a nonlinear parabolic equation with a nonlinear term involving the state and the gradient in unbounded domains

Abstract

In this paper, we consider the existence of insensitizing control for a semilinear heat equation involving gradient terms in unbounded domain OO. In this case, we prove the existence of controls insensitizing the L2L2-norm of the observation of the solution in an open subset of the domain. The proofs of the main results in this paper involve such inequalities and rely on the study of these linear problems and appropriate fixed point arguments.