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Fourier and Tikhonov regularization methods for solving a class of backward heat conduction problems. (Chinese. English summary) Zbl 1150.35591
Summary: A class of one-dimensional backward heat conduction problems are discussed and a Fourier regularization approximating solution with Hölder type stability estimate is given. Moreover, by improving the a priori assumption, a Tikhonov regularization approximating solution with logarithmic type stability estimate is also given and the convergence of the solution at \(t=0\) is proved.

MSC:
35R25 Ill-posed problems for PDEs
35R30 Inverse problems for PDEs
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