Determination of an unknown diffusion coefficient in a semilinear parabolic problem

A semilinear parabolic problem of second order with an unknown diffusion coefficient in a subregion is considered. The missing data are compensated by a total flux condition through a given surface. The solvability of this problem is proved. A numerical algorithm based on Rothe's method is designed and the convergence of approximations towards the solution is shown. The results of numerical experiments are discussed.