Numerical investigation of the Showalter–Sidorov problem for nonlinear diffusion equation

The article concerns a numerical investigation of nonlinear diffusion model in the circle. Nonlinear diffusion equation simulates the change of potential concentration of viscoelastic fluid, which is filtered in a porous media. This equation is a semilinear Sobolev type equation. Sobolev type equations constitute a vast area of non-classical equations of mathematical physics. Theorem of existence and uniqueness of a weak generalized solution to the Showalter–Sidorov problem for nonlinear diffusion equation is stated. The algorithm of numerical solution to the problem in a circle was developed using the modified Galerkin method. There is a result of computational experiment in this article.