Some uniqueness theorems for inverse spacewise dependent source problems in nonlinear PDEs

We investigate the uniqueness of a solution for an inverse problem of determining a spacewise-dependent source in some non-linear parabolic and hyperbolic problems. The material coefficients appearing in the governing equations may depend on both space and time. The aim is to identify a spacewise-dependent source from the usual initial and boundary conditions and the final-time over-determination. We formulate conditions on coefficients which guarantee the uniqueness of a solution of the inverse problem.