Universal Journal of Computational Mathematics(CEASE PUBLICATION) Vol. 5(1), pp. 1 - 7
DOI: 10.13189/ujcmj.2017.050101
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To the Properties of the Solutions of a Cross-diffusion Parabolic System not in Divergence Form


Mirsaid Aripov , Alisher Matyakubov *
Department of Applied Mathematics and Computer Analysis, National University of Uzbekistan, Tashkent, Uzbekistan

ABSTRACT

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.

KEYWORDS
Cross-diffusive System, Not in Divergence Form, Finite Speed, Perturbation, Asymptotic Behavior, Numerical Analysis

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mirsaid Aripov , Alisher Matyakubov , "To the Properties of the Solutions of a Cross-diffusion Parabolic System not in Divergence Form," Universal Journal of Computational Mathematics(CEASE PUBLICATION), Vol. 5, No. 1, pp. 1 - 7, 2017. DOI: 10.13189/ujcmj.2017.050101.

(b). APA Format:
Mirsaid Aripov , Alisher Matyakubov (2017). To the Properties of the Solutions of a Cross-diffusion Parabolic System not in Divergence Form. Universal Journal of Computational Mathematics(CEASE PUBLICATION), 5(1), 1 - 7. DOI: 10.13189/ujcmj.2017.050101.