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

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.

arXiv comment17 pages, to be published in Journal of Inverse and Ill-posed Problems

References in corpus (1)

• Inverse problems for two by two reaction-diffusion system using a Carleman estimate with one observation

Cited by in corpus (4)

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• Identification of source terms in wave equation with dynamic boundary conditions
• Finite-time stabilization and impulse control of heat equation with dynamic boundary conditions