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The application of domain derivative for heat conduction with mixed condition in shape reconstruction. (English) Zbl 1112.65092

The authors investigate the inverse problem of detecting a cavity within a potential field by measuring the Cauchy data on the exterior known boundary. Notably, the boundary conditions on the cavity are of mixed type. No uniqueness result is mentioned. The domain derivative follows closely references [F. Hettlich and W. Rundell, Inverse Probl. 12, No. 3, 251–266 (1996; Zbl 0858.35134); F. Hettlich, ibid. 11, No. 2, 371–382 (1995); erratum ibid. 14, 209–210 (1998; Zbl 0821.35147) and F. Hettlich and W. Rundell, ibid. 17, No. 5, 1465–1482 (2001; Zbl 0986.35129)]. Section 3 is quite incomplete, e.g. no justification how one chooses the regularization parameter \(\alpha\) and the numbers \(M\), \(Q\), \(\rho_1\), \(\rho_2\).

MSC:

65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35R30 Inverse problems for PDEs
35K05 Heat equation
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