NUMERICAL INVESTIGATION OF THE SHOWALTER - SIDOROV PROBLEM FOR NONLINEAR DIFFUSION EQUATION

The article concerns a numerical investigation of nonlinear diffusion mod- el in the circle. Nonlinear diffusion equation simulates the change of potential concentration of viscoelastic fluid, which is filtered in a porous media. This equa- tion is a semilinear Sobolev type equation. Sobolev type equations constitute a vast area of non-classical equations of mathematical physics. Theorem of exis- tence 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.

nonlinear diffusion equation, numerical modelling, Galerkin’s method, Sobolev type equations, Showalter – Sidorov problem, weak