Insensitizing controls of a volume-surface reaction-diffusion equation with dynamic boundary conditions

Abstract

This paper deals with the insensitizing controllability property of the quasilinear parabolic equation with dynamic boundary conditions. This problem can be reformulated as a null controllability problem for a cascade quasilinear system with dynamic boundary conditions. To this end, we approach the problem by first dealing with null controllability in the framework of an inhomogeneous linearized system. Next, we derive new estimates of control and state, allowing us to apply a local inversion theorem to obtain null controllability of the quasilinear system.