An Inverse Problem for a Nonlinear Diffusion Equation

In this paper we consider the determination of an unknown diffusion coefficient in a nonlinear diffusion equation from overspecified data measured at the boundary. This inverse problem is reformulated as an “auxiliary inverse problem,” where we seek a member of a class of admissible coefficients which minimizes a given error functional. It is shown that this auxiliary problem has at least one solution in a specified admissible class. Finally, the auxiliary problem is approximated by an associated identification problem and some numerical results are presented.