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arXiv · 0710.2192

Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates

Sergio Vessella
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Abstract

In this paper we will review the main results concerning the issue of stability for the determination unknown boundary portion of a thermic conducting body from Cauchy data for parabolic equations. We give detailed and selfcontained proofs. We prove that such problems are severely ill-posed in the sense that under a priori regularity assumptions on the unknown boundaries, up to any finite order of differentiability, the continuous dependence of unknown boundary from the measured data is, at best, of logarithmic type.

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Sergio Vessella. 2007-10-11. Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates. https://doi.org/10.1088/0266-5611%2F24%2F2%2F023001

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