Assume that a Robin boundary condition models the presence of defects in the thermal (or electric) insulation of the top side of the open rectangular domain $\Omega$. The temperature fulfills Laplace's equation. Here we study the inverse problem of recovering the heat exchange coefficient $\gamma$ in the Robin condition, from the knowledge of a Cauchy data set on the bottom side of $\Omega$. We derive logaritmic stability estimates under suitable apriori informtation about \gamma and discuss the relation between the stability of solutions and thickness of domain.
Stability of the solution of an inverse problem for Laplace's equation in a thin strip
Gabriele Inglese
2001
Abstract
Assume that a Robin boundary condition models the presence of defects in the thermal (or electric) insulation of the top side of the open rectangular domain $\Omega$. The temperature fulfills Laplace's equation. Here we study the inverse problem of recovering the heat exchange coefficient $\gamma$ in the Robin condition, from the knowledge of a Cauchy data set on the bottom side of $\Omega$. We derive logaritmic stability estimates under suitable apriori informtation about \gamma and discuss the relation between the stability of solutions and thickness of domain.File in questo prodotto:
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