Geodesic
On the Asymptotic Behavior of Solutions of Nonlinear Second-Order Parabolic Equations
Informatics and Automation, 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. 
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V. A. Kondrat'ev. On the Asymptotic Behavior of Solutions of Nonlinear Second-Order Parabolic Equations. Informatics and Automation, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 180-192. http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a11/

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