Monotonicity and Uniqueness Results in Identifying an Unknown Coefficient in a Nonlinear Diffusion Equation

We consider the problem of identifying an unknown diffusion coefficient in a nonlinear diffusion equation from overspecified data measured on the boundary. Conditions ensuring compatibility of the data are derived and it is shown that the mapping which carries the diffusion coefficient into the data is isotonic. This result is then used to derive a uniqueness result for the inverse problem and for an associated identification problem. Some results of numerical experiments are presented to illustrate the various results.