Finite Speed of the Perturbation Distribution and Asymptotic Behavior of the Solutions of a Parabolic System not in Divergence Form

The property of a finite speed of a perturbation distribution to the Cauchy problem for a parabolic system not in divergence form based on comparison method and an asymptotic behavior of a self-similar solution for both slow and fast diffusion cases are established. It is shown that the coefficients of the main term of the asymptotic of solution satisfy some system of nonlinear algebraic equations. It is found the Zeldovich-Kompaneets-Barenblatt type solution to the parabolic system.

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