Recovering memory kernels in parabolic transmission problems

In this paper we recover two unknown kernels related to a thermal body Ω with memory consisting of two different sub-bodies Ω 1 and Ω 2 , when the boundaries of Ω 1 and Ω 2 have a common (closed) surface Γ intersecting the boundary ∂Ω of Ω. The additional measurements are performed on two (accessible) subsets of ∂Ω 1 and ∂Ω 2 . 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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