An inverse fluid--solid interaction problem

Peter Monk; Virginia Selgas

doi:10.3934/ipi.2009.3.173

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2009, Volume 3, Issue 2: 173-198. Doi: 10.3934/ipi.2009.3.173

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An inverse fluid--solid interaction problem

Peter Monk^1, and
Virginia Selgas^2,

1.
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716
2.
Departamento de Matemáticas, Universidad de A Coruña, 15707 A Coruña

Received: July 31, 2008

Revised: January 31, 2009

Published: April 2009

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Abstract

This paper is devoted to studying the Linear Sampling Method (LSM) applied to the inverse problem for the fluid-solid interaction problem of determining the shape of the solid from far field measurements of the fluid pressure field. We provide a simplified proof of the uniqueness problem in this case, an analysis of the appropriate interior transmission problem, and the existence of a solution to the LSM that can be used as an indicator for the shape of the solid. The analysis of uniqueness rests on a new technical result concerning regularity. Finally we present some numerical results for the method.

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Mathematics Subject Classification: 65N21, 74F10.

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