Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions

TL;DR

This paper establishes a Lipschitz stability result for determining coefficients in a coupled semilinear parabolic system with dynamic boundary conditions, using Carleman estimates and a single observation component.

Contribution

It introduces new Carleman estimates for dynamic boundary conditions and proves stable coefficient determination with minimal observational data.

Findings

Lipschitz stability for interior and boundary coefficients

Effective method using a single localized observation

New Carleman estimates for surface diffusion boundary conditions

Abstract

In this work, we study the stable determination of four space-dependent coefficients appearing in a coupled semilinear parabolic system with variable diffusion matrices subject to dynamic boundary conditions which couple intern-boundary phenomena. We prove a Lipschitz stability result for interior and boundary potentials by means of only one observation component, localized in any arbitrary open subset of the physical domain. The proof mainly relies on some new Carleman estimates for dynamic boundary conditions of surface diffusion type.