Abstract:
In this article we examine in Sobolev spaces well-posedness questions of inverse problems of recovering the heat transfer coefficient from a collection of integrals of a flux with weight over the boundary. Under some conditions we demonstrate that a unique solution to the problem exists locally in time and depends continuously on the data. The method is constructive and the proposed approach allows us to construct new numerical methods for determining a solution. The proof employs a priori bounds and the contraction mapping principle.
Keywords:parabolic equation, heat transfer coefficient, inverse problem, existence, uniqueness
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