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Ufimskii Matematicheskii Zhurnal, 2011, Volume 3, Issue 4, Pages 64–85
(Mi ufa119)
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This article is cited in 7 scientific papers (total in 7 papers)
Estimates of solutions of an anisotropic doubly nonlinear parabolic equation
L. M. Kozhevnikova, A. A. Leontiev Sterlitamak State Pedagogical Academy, Sterlitamak, Russia
Abstract:
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 $\Omega\subset\mathbb R_n$, $n\geq3$, are established when $t\to\infty$. Existence of strong solutions is proved by the method of Galerkin's approximations. The method of their construction for the modelling 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 basis of Galerkin's approximations. It proves the accuracy of the upper estimate.
Keywords:
anisotropic equation, doubly nonlinear parabolic equations, existence of strong solution, decay rate of solution.
Received: 15.07.2011
Citation:
L. M. Kozhevnikova, A. A. Leontiev, “Estimates of solutions of an anisotropic doubly nonlinear parabolic equation”, Ufa Math. J., 3:4 (2011)
Linking options:
https://www.mathnet.ru/eng/ufa119 https://www.mathnet.ru/eng/ufa/v3/i4/p64
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