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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.

MSC:
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
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