# Article

Ufa Mathematical Journal
Volume 3, Number 4, pp. 62-83

# Estimates of solutions of anisotropic doubly nonlinear parabolic equation

Kozhevnikova L.M., Leontiev A.A.

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## Abstact

In this work the first mixed problem with the Dirihlet ho\-mo\-ge\-neous boundary condition and finite initial function for some class of the second order anisotropic doubly nonlinear parabolic equations is considered in cylindrical domain $D=(0,\infty)\times\Omega$ . Upper estimates characterizing a dependence of decay rate of solution to the problem on geometry of unbounded domain $\Omega\subset \mathbb{R}_n,\;n\geq 3$ are established as $t\rightarrow\infty$. Existence of strong solutions is proved by the method of Galerkin's approximations which way of construction for the modelling isotropic equation early has been offered by F.Kh. Mukminov. The estimate of admissible decay rate of the solution on unbounded domain has been received on a basis of Galerkin's approximations, proves accuracy of the upper estimate.