To the Properties of the Solutions of a Cross-diffusion Parabolic System not in Divergence Form
Мирсаид АриповDepartment of Applied Mathematics and Computer Analysis, National University of Uzbekistan, Tashkent, UzbekistanAlisher MatyakubovDepartment of Applied Mathematics and Computer Analysis, National University of Uzbekistan, Tashkent, Uzbekistan
ABI
Annotatsiya
The Zeldovich-Barenblatt type solution of the Cauchy problem for a cross-diffusion parabolic system not in divergence form with a source and a variable density is obtained. Based on comparison method the property of finite speed perturbation of distribution is considered. An asymptotic behavior of self-similar solutions, both for slow and fast diffusion cases, is established. It is obtained the system of the nonlinear algebraic equations with the coefficients of the main terms of the asymptotical solution.
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