Carleman estimate and inverse source problem for Biot's equations describing wave propagation in porous media

摘要

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 Lamé 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 sub-domain along a sufficiently large time interval. Our main result is a H?lder stability estimate for the inverse source problem, which is proved by a new Carleman estimate for Biot's system.