Geodesic
Numerical investigation of the Showalter--Sidorov problem for nonlinear diffusion equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2015), pp. 24-28

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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, Showalter–Sidorov problem, weak generalized solution, monotone operators, monotone method.
Mots-clés : Sobolev type equations 
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     author = {N. A. Manakova and A. A. Selivanova},
     title = {Numerical investigation of the {Showalter--Sidorov} problem for nonlinear diffusion equation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {24--28},
     publisher = {mathdoc},
     number = {10},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2015_10_a1/}
}
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N. A. Manakova; A. A. Selivanova. Numerical investigation of the Showalter--Sidorov problem for nonlinear diffusion equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2015), pp. 24-28. http://geodesic.mathdoc.fr/item/VSGU_2015_10_a1/