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

E. M. Ait Ben Hassi, S. E. Chorfi, L. Maniar

Published 2021-03-28Version 1

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.