An Inverse Problem for a Nonlinear Parabolic Equation with Applications in Population Dynamics and Magnetics

The parabolic equation of this paper is a nonlinear one with the unknown coefficient depending on the derivative of the solution. A uniqueness result is proven by the method of Carleman estimates. The applicability of this result is illustrated for parameter identification problems in population dynamics and magnetics. For the latter application, we provide numerical results using a reconstruction method based on a multiharmonic formulation of the problem.