Carleman Estimate and Inverse Source Problem for Biot's Equations Describing Wave Propagation in Porous Media
Analysis of PDEs
2015-06-15 v1
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 H\"older stability estimate for the inverse source problem, which is proved by a new Carleman estimat for Biot's system.
Keywords
Cite
@article{arxiv.1304.5695,
title = {Carleman Estimate and Inverse Source Problem for Biot's Equations Describing Wave Propagation in Porous Media},
author = {Mourad Bellassoued and Masahiro Yamamoto},
journal= {arXiv preprint arXiv:1304.5695},
year = {2015}
}