najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-1-5-12najo-714Research ArticleMATHEMATICSМАТЕМАТИКАSelf-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behaviourAripovM. M.

Universitet, 4, Tashkent, 100174

mirsaidaripov@mail.ruMatyakubovA. S.

Universitet, 4, Tashkent, 100174

almasa@list.ruNational University of Uzbekistan, Applied Mathematics and Computer AnalysisUzbekistan20171308202581512Copyright © Aripov M.M., Matyakubov A.S., 20252025Aripov M.M., Matyakubov A.S.Aripov M.M., Matyakubov A.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/714

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 nonlinear algebraic equations.

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The authors declare that there are no conflicts of interest present.