Geodesic
On the Asymptotic Behavior of Solutions of Nonlinear Second-Order Parabolic Equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 180-192.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the asymptotic behavior as $t\to+\infty$ of solutions to a semilinear second-order parabolic equation in a cylindrical domain bounded in the spatial variable. We find the leading term of the asymptotic expansion of a solution as $t\to+\infty$ and show that each solution of the problem under consideration is asymptotically equivalent to a solution of some nonlinear ordinary differential equation. 
@article{TM_2008_260_a11,
     author = {V. A. Kondrat'ev},
     title = {On the {Asymptotic} {Behavior} of {Solutions} of {Nonlinear} {Second-Order} {Parabolic} {Equations}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {180--192},
     publisher = {mathdoc},
     volume = {260},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_260_a11/}
}
TY  - JOUR
AU  - V. A. Kondrat'ev
TI  - On the Asymptotic Behavior of Solutions of Nonlinear Second-Order Parabolic Equations
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2008
SP  - 180
EP  - 192
VL  - 260
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2008_260_a11/
LA  - ru
ID  - TM_2008_260_a11
ER  - 
%0 Journal Article
%A V. A. Kondrat'ev
%T On the Asymptotic Behavior of Solutions of Nonlinear Second-Order Parabolic Equations
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2008
%P 180-192
%V 260
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2008_260_a11/
%G ru
%F TM_2008_260_a11
V. A. Kondrat'ev. On the Asymptotic Behavior of Solutions of Nonlinear Second-Order Parabolic Equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 180-192. http://geodesic.mathdoc.fr/item/TM_2008_260_a11/

[1] Egorov Yu. V., Kondratev V. A., Oleinik O. A., “Asimptoticheskoe povedenie reshenii nelineinykh ellipticheskikh i parabolicheskikh sistem v tsilindricheskikh oblastyakh”, Mat. sb., 189:3 (1998), 45–68 | MR | Zbl

[2] Kondratiev V. A., Veron L., “Asymptotic behaviour of solutions of some nonlinear parabolic or elliptic equations”, Asymp. Anal., 14:2 (1997), 117–156 | MR | Zbl

[3] Filimonova I. V., “Asimptotika reshenii polulineinogo parabolicheskogo uravneniya v tsilindricheskoi oblasti”, Mat. sb., 195:2 (2004), 141–156 | MR | Zbl

[4] Boni T. K., “On the asymptotic behavior of solutions for some semilinear parabolic and elliptic equations of second order with nonlinear boundary conditions”, Nonlin. Anal. Theory, Meth. and Appl., 45 (2001), 895–908 | DOI | MR | Zbl

[5] Filimonova I. V., “O povedenii reshenii polulineinogo parabolicheskogo ili ellipticheskogo uravneniya, udovletvoryayuschikh nelineinomu kraevomu usloviyu v tsilindricheskoi oblasti”, Tr. sem. im. I. G. Petrovskogo, 26 (2007), 368–389

[6] Moser J., “A Harnack inequality for parabolic differential equations”, Commun. Pure and Appl. Math., 17 (1964), 101–134 | DOI | MR | Zbl

[7] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967 | MR | Zbl