Two-dimensional inverse heat conduction problem in a quarter plane: integral approach. (English) Zbl 1479.35939
Summary: We consider a two-dimensional inverse heat conduction problem in the region \(\lbrace x>0, y >0 \rbrace\) 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 \(g_\delta\) of exact data \(g\). We show some numerical examples to illustrate the validity of the method.
MSC:
| 35R30 | Inverse problems for PDEs |
| 35K05 | Heat equation |
| 47A52 | Linear operators and ill-posed problems, regularization |
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
Keywords:
heat equation; inverse problem; integral equations; Tikhonov regularization; mollification of the noised dataSoftware:
Regularization toolsReferences:
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