Determination of a two-dimensional heat source: uniqueness, regularization and error estimate. (English) Zbl 1096.65097
The authors consider the problem of finding a two-dimensional heat source having the form \(\phi(t)f(x,t)\) in a heat conduction body \(Q\). Assuming \(\partial Q\) is insulated and \(\phi\neq 0\), the authors show that the heat source is defined uniquely by the temperature history on \(\partial Q\) and the temperature distribution in \(Q\) at the initial time \(t=0\) and the final time \(t=1\). Using the method of truncated integration and the Fourier transform, the authors construct regularization solutions and derive explicitly an error estimate.
Reviewer: Andrey L. Karchevsky (Novosibirsk)
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 35K05 | Heat equation |
| 35R30 | Inverse problems for PDEs |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
error estimate; Fourier transform; ill-posed problems; heat-conduction; heat source; truncated integration; inverse problemReferences:
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