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Stability analysis of an inverse parabolic problem with discontinuous variable coefficient

Published online by Cambridge University Press:  26 September 2011

M. Di Cristo  and
S. Vessella
M. Di Cristo
Affiliation:
Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy (michele.dicristo@polimi.it)
S. Vessella
Affiliation:
Dipartimento di Matematica per le Decisioni, Università di Firenze, via Lombroso 6/17, 50134 Firenze, Italy (sergio.vessella@dmd.unifi.it)
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Abstract

We consider a time-varying inclusion in a thermal conductor specimen. In particular, the thermal conductivity is a variable function depending on space and time with a jump of discontinuity along the interface of the unknown anomalous region. Provided with some a priori information on the conductivity and its support, we study the continuous dependence of the inclusion from infinitely many thermal measurements taken on an open portion of the boundary of our specimen. We prove a rate of continuity of logarithmic type showing, in addition, its optimality.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 5 , October 2011 , pp. 975 - 999
Copyright
Copyright © Royal Society of Edinburgh 2011

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