Nonlinear wave inverse source problem solved by a method of m-order homogenization functions

Abstract

Abstract We solve the inverse source problem of a nonlinear wave equation, developing a family of m -order homogenization functions. When the solution is solved using the superposition of the homogenization functions, the unknown space–time dependent wave source function can be recovered by solving an m -dimensional small scale linear system. The data overspecified to recover the wave source function are final time data and strain on the right side. The present method does not need the iteration to solve nonlinear equations, which is quite accurate for simultaneously solving the solution and the unknown wave source function in the whole domain, even the noise is imposed on the overspecified data.