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.
Stability analysis of an inverse parabolic problemwith discontinuous variable coefficient / M. Di Cristo; S. Vessella. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - STAMPA. - 141A:(2011), pp. 975-999. [10.1017/S0308210510000466]
Stability analysis of an inverse parabolic problemwith discontinuous variable coefficient
VESSELLA, SERGIO
2011
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.File | Dimensione | Formato | |
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