Research On Inverse Problems For Piezoelectric Equation

The main purpose of this work is to study an inverse source and inverse coeffi-cient problem for piezoelectric equation in one dimension which is of great interest in nanomaterials.Firstly,provided that additional measurement data are given on an interior sub-domain with non-vanishing measure,get the Carleman estimate for the decoupled piezoelectric equations in one dimensional case.Furthermore,based on the estimate obtained above and two first order partial differential operators'Carleman estimate,Holder for the inverse source and coeffi-cient problems are obtained respectively.In the end,a numerical algorithm based upon conjugate-gradient method is investigated for the corresponding inverse source and coefficient problems.Nu-merical examples are presented to demonstrate the effectiveness of the proposed algorithm.