Xiang Xu, Professor, Zhejiang University

Tao Yin，Associate Professor

Inverse Problems on Piezoelectric Equations

14:00-14:45 December 20（Tuesday）, Tencent Meeting ID: 567 855 609

In this talk, recent progress on inverse problems for piezoelectric equations is discussed. We show a uniqueness result on recovering coefficients of piecewise homogeneous piezoelectric equations from a localized Dirichlet-to-Neumann map on partial boundaries. Assume the bounded domain can be divided into finite subdomains, in which the unknown coefficients including elastic tensor, piezoelectric tensor and dielectric tensor are constants. Two different cases are considered: the subdomains are either known and Lipschitz, or unknown and subanalytic. For both cases, the unknown coefficients can be uniquely determined from a given localized Dirichlet-to-Neumann map. Moreover, for a specific hexagonal piezoelectric equation, we obtained a first order perturbation formula for the phase velocity of Bleustein-Gulyaev (BG) waves, which expresses the shift in the velocity from its comparative value, caused by the perturbation of the elasticity tensor, the piezoelectric tensor and of the dielectric tensor.