NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2017, 8 (1), P. 5–12
Self-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behaviour
M. M. Aripov – National University of Uzbekistan, Applied Mathematics and Computer Analysis, Universitet, 4, Tashkent, 100174, Uzbekistan; firstname.lastname@example.org
A. S. Matyakubov – National University of Uzbekistan, Applied Mathematics and Computer Analysis, Universitet, 4, Tashkent, 100174, Uzbekistan; email@example.com
In this paper, we study the properties of self-similar solutions of a cross-diffusion parabolic system. In particular, we find the Zeldovich–Barenblatt type solution to the cross diffusive system. The asymptotic behavior of self-similar solutions are analyzed for both the slow and fast diffusive regimes. It is shown that coefficients of the main term of the asymptotic of solution satisfy some system of non-linear algebraic equations.
Keywords: cross-diffusive system, non-divergence form, finite speed, perturbation, global solutions, asymptotic behavior, numerical analysis.
PACS 02.30.Jr, 02.30.Mv, 11.10.Jj, 11.10.Lm