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
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.
anisotropic equation, doubly nonlinear parabolic equations, existence of strong solution, decay rate of solution.
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L. M. Kozhevnikova, A. A. Leontiev, “Estimates of solutions of an anisotropic doubly nonlinear parabolic equation”, Ufimsk. Mat. Zh., 3:4 (2011), 64–85
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\by L.~M.~Kozhevnikova, A.~A.~Leontiev
\paper Estimates of solutions of an anisotropic doubly nonlinear parabolic equation
\jour Ufimsk. Mat. Zh.
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L. M. Kozhevnikova, A. A. Leontev, “Resheniya anizotropnykh parabolicheskikh uravnenii s dvoinoi nelineinostyu v neogranichennykh oblastyakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 82–89
L. M. Kozhevnikova, A. A. Leontiev, “Decay of solution of anisotropic doubly nonlinear parabolic equation in unbounded domains”, Ufa Math. J., 5:1 (2013), 63–82
È. R. Andriyanova, F. Kh. Mukminov, “Stabilization of the solution of a doubly nonlinear parabolic equation”, Sb. Math., 204:9 (2013), 1239–1263
L. M. Kozhevnikova, A. A. Leont'ev, “Solutions to higher-order anisotropic parabolic equations in unbounded domains”, Sb. Math., 205:1 (2014), 7–44
E. R. Andriyanova, “Estimates of decay rate for solution to parabolic equation with non-power nonlinearities”, Ufa Math. J., 6:2 (2014), 3–24
L. M. Kozhevnikova, A. A. Khadzhi, “Boundedness of solutions to anisotropic second order elliptic equations in unbounded domains”, Ufa Math. J., 6:2 (2014), 66–76
A. A. Khadzhi, “Ubyvanie reshenii anizotropnykh ellipticheskikh uravnenii s mladshimi chlenami v neogranichennykh oblastyakh”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Ser. Matematika. Fizika, 34:5 (2014), 78–87
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