Determination of unknown boundary in the composite materials with Stefan-Boltzmann conditions

Abstract

The authors consider one specific kind of heat transfer problems in a three-dimensional layered domain, with nonlinear Stefan-Boltzmann conditions on the boundaries as well as on the interfaces. To determine the unknown part of the boundary (or corrosion) by the Cauchy data on the reachable part is an important inverse problem in engineering. The mathematical model of this problem is introduced, the well-posedness of the forward problems and the uniqueness of the inverse problems are obtained.

Keywords

Inverse heat problem / Stefan-Boltzmann conditions / Uniqueness

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