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

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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Received

29-09-2019

How to Cite

*Mathematical notes of NEFU*, 27(3), pp. 27-38. doi: https://doi.org/10.25587/SVFU.2020.93.40.003.

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Mathematics

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