Determination of a time-dependent diffusivity in a nonlinear parabolic problem

In this article, an inverse nonlinear convection-diffusion problem is considered for the identification of an unknown solely time-dependent diffusion coefficient in a subregion of a bounded domain in . The missing data are compensated by boundary observations on a part of the surface of the subdomain: the total flux through that surface or the values of the solution at that surface are measured. Two solution methods are discussed. In both cases, the solvability of the problem is proved using coefficient to data mappings. More specific, a nonlinear numerical algorithm based on Rothe's method is designed and the convergence of approximations towards the weak solution in suitable function spaces is shown. In the proofs, also the monotonicity methods and the Minty-Browder argument are employed. The results of numerical experiments are discussed