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

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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/}
}
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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/