A generalization of Beck’s method for Inverse Heat Conduction Problems
نویسندگان
چکیده
Inverse Heat Conduction Problems (abbr.: IHCP) occur whenever surface temperatures and surface heat fluxes should be determined at inaccessible portions of the surface from corresponding measurements at accessible parts. These problems are known to be severely illposed. There are various approaches to regularize and stabilize the illposedness (see [4, 11, 20] and the references therein). An IHCP may be considered as a non-characteristic Cauchy problem for parabolic equations, the solvability is known only for special cases (see [25, 12]). Stability estimates of Hölder type for non-characteristic Cauchy problems for the heat equation are given in [2, 3, 4, 6, 7, 22, 27] and for parabolic equations with coefficients depending smoothly on t in [8, 23, 26, 28, 29, 30, 35]. Some related results can also be found in [31, 32].
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