An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions

TL;DR

This paper addresses an inverse problem in parabolic equations with dynamic boundary conditions, establishing stability estimates for recovering radiative potentials and initial temperatures from partial observations.

Contribution

It introduces new stability results for simultaneously recovering radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions.

Findings

Lipschitz stability estimate for radiative potentials

Logarithmic stability for initial temperatures

Applicable to observations in arbitrary subdomains

Abstract

We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability estimate for the relevant potentials using a recent Carleman estimate, and a logarithmic stability result for the initial temperatures by a logarithmic convexity method, based on observations in an arbitrary subdomain.