The inverse problem for a layered anisotropic half space
Considered is the inverse problem of determining the elastic module and density of a medium for a system of partial differential equations of elasticity in a half space \({x\in \mathbb{R}^3; x_3 >0}\). It is assumed that the medium is layered, i.e., the unknown coefficients which characterize the medium are functions of \(x_3\). The additionally symmetry property implies that the module of elasticity is a symmetric matrix, thus there are at most 21 independent elements. The authors consider a special type of anisotropy, cubical with three and hexagonal with five independent elastic modules. The authors prove the possibility of a unique determination of some unknown coefficient functions from measurements of the displacement of the field for \(x\) in the surface \(x_3>0\) and in a finite time interval.
partial differential equations of elasticity
scientific article; zbMATH DE number 1246325