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An inverse diffusion problem with nonlocal boundary conditions
Author(s) -
Ismailov Mansur I.,
Oğur Bülent
Publication year - 2016
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22007
Subject(s) - mathematics , crank–nicolson method , inverse problem , boundary value problem , partial differential equation , heat equation , mathematical analysis , thermal diffusivity , inverse , boundary (topology) , finite difference , diffusion , finite difference method , thermodynamics , physics , geometry
This article considers the inverse problem of identification of a time‐dependent thermal diffusivity together with the temperature in an one‐dimensional heat equation with nonlocal boundary and integral overdetermination conditions when a heat exchange takes place across boundary of the material. The well‐posedness of the problem is studied under some regularity, and consistency conditions on the data of the problem together with the nonnegativity condition on the Fourier coefficients of the initial data and source term. The inverse problem is also studied numerically by using the Crank–Nicolson finite difference scheme combined with predictor‐corrector technique. The numerical examples are presented and discussed. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 564–590, 2016