Well posedness of a time-difference scheme for a degenerate fastdiffusion problem
Gabriela Marinoschi · Discrete and Continuous Dynamical Systems - B · 2009
We study a time-difference scheme for a nonlinear degenerateparabolic equation with a transport term. The model generallydescribes diffusion in porous media with the formation of a freeboundary, this being expressed by the presence of a multivaluedfunction in the equation. We consider singular boundary conditionswhich contain the multivalued function as well, and prove thestability and the convergence of the scheme, emphasizing the precisenature of the convergence. This approach is aimed to be amathematical background which justifies the correctness of thenumerical algorithm for computing the solution to this type ofequations by avoiding the approximation of the multivalued function.The theory is illustrated by numerical results which put intoevidence both the effects due to the equation degeneration and theformation and advance of the free boundary.