The cost of approximate controllability of heat equation with dynamical boundary conditions

TL;DR

This paper investigates the minimal control effort required to approximately steer the heat equation with dynamic boundary conditions, using advanced Carleman estimates and optimization methods for both linear and semilinear cases.

Contribution

It introduces new Carleman estimates and optimization techniques to derive explicit bounds on control costs for heat equations with dynamic boundary conditions.

Findings

Derived explicit bounds for control costs.

Extended analysis to both linear and semilinear heat equations.

Developed new Carleman estimates for dynamic boundary conditions.

Abstract

We consider the heat equation with dynamic bounary conditions involving gradient terms in a bounded domain. In this paper we study the cost of approximate controllability for this equation. Combining new developed Carleman estimates and some optimization techniques, we obtain explicit bounds of the minimal norm control. We consider the linear and the semilinear cases.