The Cauchy problem for a nonlinear degenerate parabolic system in non-divergence form

  • Aripov Mersaid M., mirsaidaripov@mail.ru National University of Uzbekistan University street 4, Tashkent 100174, Uzbekistan
  • Matyakubov Alisher S., almasa@list.ru National University of Uzbekistan University street 4, Tashkent 100174, Uzbekistan
  • Imomnazarov Bunyod Kh., buned11998.07@mail.ru Novosibirsk State University, 1 Pirogov Street, Novosibirsk 630090, Russia
Keywords: a nonlinear degenerate parabolic system, non-divergence form, Cauchy problem

Abstract

We deal with degenerate quasilinear parabolic systems in the non-divergence form under positive initial conditions. An asymptotic behavior of self-similar solutions in the case of slow diffusion is established. Depending on values of the numerical parameters and the initial value, the existence of the global solutions of the Cauchy problem is proved. In addition, the asymptotic representation of the solution is obtained.

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How to Cite
Aripov, M., Matyakubov, A. and Imomnazarov, B. (2020) “The Cauchy problem for a nonlinear degenerate parabolic system in non-divergence form”, Mathematical notes of NEFU, 27(3), pp. 27-38. doi: https://doi.org/10.25587/SVFU.2020.93.40.003.
Section
Mathematics