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Recovery of Non-smooth Radiative Coefficient from Nonlocal Observation by Diffusion System by Mengmeng Zhang; Jijun Liu is a Mathematics article available to read on EtoBox.

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## Abstract The heat conduction process in composite medium can be modeled by a parabolic equation with discontinuous radiative coefficient. To detect the composite medium characterized by such a non-smooth coefficient from measurable information about the heat distribution, we consider a nonlinear inverse problem for parabolic equation, with the average measurement of temperature field in some time interval as the inversion input. We firstly establish the uniqueness for this nonlinear inverse problem, based on the property of the direct problem and the known uniqueness result for linear inverse source problem. To solve the inverse problem from a nonlinear operator equation, the differentiability and the tangential condition of this nonlinear map is analyzed. An iterative process called two-point gradient method is proposed by minimizing data-fit term and the penalty term alternatively, with rigorous convergence analysis in terms of the tangential condition. Numerical simulations are presented to illustrate the effectiveness of the proposed method.

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Author

Mengmeng Zhang; Jijun Liu

Publisher

Walter de Gruyter GmbH

Published

2020

Language

EN

Field

Mathematics (Physical Sciences)