Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates - Mathematics > Analysis of PDEsReport as inadecuate




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Abstract: In this paper we will review the main results concerning the issue ofstability for the determination unknown boundary portion of a thermicconducting body from Cauchy data for parabolic equations. We give detailed andselfcontained proofs. We prove that such problems are severely ill-posed in thesense that under a priori regularity assumptions on the unknown boundaries, upto any finite order of differentiability, the continuous dependence of unknownboundary from the measured data is, at best, of logarithmic type.



Author: Sergio Vessella

Source: https://arxiv.org/







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