Mathematics

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

N. A. Manakova, A. A. Selivanova

South Ural State University, 76, Lenin Prospect, Chelyabinsk, 454080, Russian Federation

Abstract: 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.

Keywords: nonlinear diffusion equation, numerical modelling, Galerkin's method, Sobolev type equations, Showalter–Sidorov problem, weak generalized solution, monotone operators, monotone method.

UDC: 517.9

Received: 20.09.2015

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