On an overdetermined problem of determining parameter in a degenerate parabolic equation

This work is concerned with the solvability of the ill-posed problem of determining the diffusion velocity in nonlinear diffusion process with an additional restriction. We first prove the continuous dependence of the solutions with respect to the nonlinearity of the equation and give an explicit error-estimate formula, and then, we show the existence of the solution to the ill-posed problem and estimate the range of the velocity.