Abstract:
The first mixed problem with homogeneous Dirichlet boundary condition and initial function with compact support is considered for quasilinear second order parabolic equations in a cylindrical domain D=(0,∞)×ΩD=(0,∞)×Ω. Upper bounds are obtained, which give the rate of decay of the solutions as t→∞t→∞ as a function of the geometry of the unbounded domain Ω⊂Rn, n⩾2.
Bibliography: 18 titles.
Keywords:
first mixed problem, quasilinear parabolic equations, unbounded domain, stabilization of the solution, geometric characteristic.
Citation:
R. Kh. Karimov, L. M. Kozhevnikova, “Stabilization of solutions of quasilinear second order parabolic equations in domains with non-compact boundaries”, Sb. Math., 201:9 (2010), 1249–1271
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\paper Stabilization of solutions of quasilinear second order parabolic equations in domains with non-compact boundaries
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\pages 1249--1271
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This publication is cited in the following 11 articles:
È. R. Andriyanova, F. Kh. Mukminov, “Existence and qualitative properties of a solution of the first mixed problem for a parabolic equation with non-power-law double nonlinearity”, Sb. Math., 207:1 (2016), 1–40
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
D. Andreucci, A. F. Tedeev, “The Cauchy-Dirichlet problem for the porous media equation in cone-like domains”, SIAM J. Math. Anal., 46:2 (2014), 1427–1455
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, F. Kh. Mukminov, “Stabilization of solutions of an anisotropic quasilinear parabolic equation in unbounded domains”, Proc. Steklov Inst. Math., 278 (2012), 106–120
E. R. Andriyanova, F. Kh. Mukminov, “Otsenka snizu skorosti ubyvaniya resheniya parabolicheskogo uravneniya s dvoinoi nelineinostyu”, Ufimsk. matem. zhurn., 3:3 (2011), 3–14
V. F. Gilimshina, F. Kh. Mukminov, “Ob ubyvanii resheniya vyrozhdayuschegosya lineinogo parabolicheskogo uravneniya”, Ufimsk. matem. zhurn., 3:4 (2011), 43–56
L. M. Kozhevnikova, A. A. Leontev, “Otsenki resheniya anizotropnogo parabolicheskogo uravneniya s dvoinoi nelineinostyu”, Ufimsk. matem. zhurn., 3:4 (2011), 64–85
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