Carleman estimates and the contraction principle for an inverse source problem for nonlinear hyperbolic equations

The main aim of this paper is to solve an inverse source problem for a general nonlinear hyperbolic equation. Combining the quasi-reversibility method and suitable Carleman weight function, we define map which fixed point solution problem. To find point, recursive sequence with arbitrary initial term by same manner as in classical proof contraction principle. Applying estimate, show that above converges desired exponential rate. Therefore, our new can be considered analog We rigorously study stability respect noise. Numerical examples are presented.