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Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem. (English) Zbl 1208.65141
Summary: We propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel is adopt to provide a stable solution when the measurement data contain noises. Numerical results indicate that the proposed method is stable, efficient, and accurate.

65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R30 Inverse problems for PDEs
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
80A23 Inverse problems in thermodynamics and heat transfer
65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
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