A parabolic inverse source problem with a dynamical boundary condition

M. Slodička

Applied Mathematics and Computation, 2015, vol. 256, issue C, 529-539

Abstract: An inverse source problem for the heat equation is studied in a bounded domain. A dynamical nonlinear boundary condition (containing the time derivative of a solution) is prescribed on one part of the boundary. This models a non-perfect contact on the boundary. The missing purely time-dependent source is recovered from an additional integral measurement. The global in time existence and uniqueness of a solution in corresponding function spaces is addressed using the backward Euler method for the time discretization. Error estimates for time-discrete approximations are derived.

Keywords: Heat equation; Inverse source problem; Time discretization; Error estimates (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:256:y:2015:i:c:p:529-539

DOI: 10.1016/j.amc.2015.01.103

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