A homotopy strategy for the parameter identification problems of partial differential equations

The aim of this paper is to propose a general homotopy inversion strategy for solving the inverse problems of partial differential equations, which reduces solving the inverse problems to a task of tracing a class of inverse problems continuously, and then solving the corresponding class of operator equations. On the basic of this strategy, a differentiation regularization method and a homotopy regularization method are constructed. Some theoretical results are given. As a practical application, the inverse problem of a two-dimensional wave equation is solved. Numerical results show the method's effectiveness.