# American Institute of Mathematical Sciences

May  2009, 3(2): 173-198. doi: 10.3934/ipi.2009.3.173

## An inverse fluid--solid interaction problem

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

Received  August 2008 Revised  February 2009 Published  May 2009

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.
Citation: Peter Monk, Virginia Selgas. An inverse fluid--solid interaction problem. Inverse Problems and Imaging, 2009, 3 (2) : 173-198. doi: 10.3934/ipi.2009.3.173
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