AN INVERSE COEFFICIENT PROBLEM FOR A NONLINEAR REACTION DIFFUSION EQUATION WITH A NONLINEAR SOURCE

In this article, we consider the problem of identifying an unknown coefficient in a nonlinear diffusion equation. Under appropriate conditions, we prove the existence and the uniqueness of solution for the inverse problem. For the numerical solution of the inverse problem, a numerical method based on discretization of the minimization problem, steepest descent method and least squares approach is proposed. A numerical example is given to illustrate applicability and high accuracy of the proposed method.