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

TL;DR

This paper investigates insensitizing controllability for a quasilinear parabolic PDE with dynamic boundary conditions, introducing new estimates and a local inversion approach to achieve null controllability.

Contribution

It develops a novel method combining linearized controllability and local inversion to handle quasilinear systems with dynamic boundary conditions.

Findings

Establishes null controllability for the linearized system.

Derives new control and state estimates.

Achieves null controllability for the quasilinear system.

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.