Two-dimensional inverse heat conduction problem in a quarter plane: integral approach

We consider a two-dimensional inverse heat conduction problem in the region { x > 0 , y > 0 } with infinite boundary which consists to reconstruct the boundary condition f ( y , t ) = u ( 0 , y , t ) on one side from the measured temperature g ( y , t ) = u ( 1 , y , t ) on accessible interior...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2020-02, Vol.62 (1-2), p.565-586
Main Authors: Bel Hadj Hassin, Anis, Chorfi, Lahcène
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary conditions
Boundary element method
Boundary integral method
Computational Mathematics and Numerical Analysis
Conduction heating
Conductive heat transfer
Ill posed problems
Integral equations
Inverse problems
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Original Research
Regularization
Theory of Computation
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Summary:We consider a two-dimensional inverse heat conduction problem in the region { x > 0 , y > 0 } with infinite boundary which consists to reconstruct the boundary condition f ( y , t ) = u ( 0 , y , t ) on one side from the measured temperature g ( y , t ) = u ( 1 , y , t ) on accessible interior region. The numerical solution of the direct problem is computed by a boundary integral equation method. The inverse problem is equivalent to an ill-posed integral equation. For its approximation we use the regularization of Tikhonov after the mollification of the noised data g δ of exact data g . We show some numerical examples to illustrate the validity of the method.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-019-01297-4