Recovering memory kernels in parabolic transmission problems

J. Janno and A. Lorenzi

Abstract

In this paper we recover two unknown kernels related to a thermal body Ω with memory consisting of two different sub-bodies Ω1 and Ω2, when the boundaries of Ω1 and Ω2 have a common (closed) surface Γ intersecting the boundary ∂Ω of Ω. The additional measurements are performed on two (accessible) subsets of ∂Ω1 and ∂Ω2. For this problem we prove existence, uniqueness and continuous dependence on the data in the framework of Sobolev spaces of L 2-type in space.

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This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.

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