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arXiv · 1304.5695

Carleman Estimate and Inverse Source Problem for Biot's Equations Describing Wave Propagation in Porous Media

Mourad Bellassoued·Masahiro Yamamoto
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Abstract

According to Biot's paper in 1956, by using the Lagrangian equations in classical mechanics, we consider a problem of the filtration of a liquid in porous elastic-deformation media whose mechanical behavior is described by the Lam'e system coupled with a hyperbolic equation. Assuming the null surface displacement on the whole boundary, we discuss an inverse source problem of determining a body force only by observation of surface traction on a suitable subdomain along a sufficiently large time interval. Our main result is a Hölder stability estimate for the inverse source problem, which is proved by a new Carleman estimat for Biot's system.

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Mourad Bellassoued, Masahiro Yamamoto. 2013-04-21. Carleman Estimate and Inverse Source Problem for Biot's Equations Describing Wave Propagation in Porous Media. https://doi.org/10.1088/0266-5611%2F29%2F11%2F115002

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