Kozhevnikova, L. M.; Leontiev, A. A. Solutions estimates of anisotropic doubly nonlinear parabolic equation. (Russian. English summary) Zbl 1249.35174 Ufim. Mat. Zh. 3, No. 4, 64-85 (2011). Summary: The first mixed problem with the Dirihlet homogeneous boundary-value condition and a finite initial function is considered for a certain class of second-order anisotropic doubly nonlinear parabolic equations in a cylindrical domain \(D=(0, \infty)\times\Omega. \) Upper estimates characterizing the dependence of the decay rate of the solution to the problem on geometry of an unbounded domain \(\Omega\subset\mathbb{R}^{n},\) \(n\geq 3\) are established when \(t\rightarrow\infty. \) Existence of strong solutions is proved by the method of Galerkin’s approximations. The method of their construction for the modeling isotropic equation has been earlier offered by F. Kh. Mukminov, E. R. Andriyanova. The estimate of the admissible decay rate of the solution on an unbounded domain has been obtained on the basic of Galerkin’s approximations. It proves the accuracy of the upper estimate. Reviewer: Boris V. Loginov (Ul’yanovsk) Cited in 3 Documents MSC: 35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations Keywords:anisotropic equation; doubly nonlinear parabolic equations; existence of strong solution; decay rate of solution × Cite Format Result Cite Review PDF Full Text: MNR