Abstract:
We consider a second order parabolic equation and the well-posedness of inverse problems of recovering the heat transfer coefficients in Sobolev spaces with the use of a collection of integrals of a solution over the boundary of a domain. Under certain conditions on the data, we demonstrate that the existence of a unique local-in-time solution that depends continuously on the data. The method is constructive and allows us to provide some numerical methods of solution. The proof employs a priori estimates and the fixed point theorem.
Keywords:inverse problem, heat transfer coefficient, parabolic equation, heat and mass transfer.
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