Geodesic
Asymptotic behaviour of solutions of
Sbornik. Mathematics, Tome 199 (2008) no. 4, pp. 539-556 
Yu. V. Egorov; V. A. Kondratiev. Asymptotic behaviour of solutions of. Sbornik. Mathematics, Tome 199 (2008) no. 4, pp. 539-556. http://geodesic.mathdoc.fr/item/SM_2008_199_4_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The asymptotic behaviour of solutions of a second-order semilinear parabolic equation is analyzed in a cylindrical domain that is bounded in the space variables. The dominant term of the asymptotic expansion of the solution as $t\to+\infty$ is found. It is shown that the solution of this problem is asymptotically equivalent to the solution of a certain non-linear ordinary differential equation. Bibliography: 8 titles.

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[5] Yu. V. Egorov, V. A. Kondratiev, On asymptotic behavior of solutions of semi-linear parabolic boundary value problems, Université Paul Sabatier, Toulouse, Labo MIP. Rapport interne, 1998, No98.08

[6] Th. K. Boni, “On the asymptotic behavior of solutions for some semilinear parabolic and elliptic equations of second order with nonlinear boundary conditions”, Nonlinear Anal., 45:7 (2001), 895–908 | DOI | MR | Zbl

[7] J.-L. Lions, E. Magenes, Problèmes aux limites non homogènes et applications, vol. 1, Dunod, Paris, 1968 ; Zh.-L. Lions, E. Madzhenes, Neodnorodnye granichnye zadachi i ikh prilozheniya, t. 1, Mir, M., 1971 | MR | Zbl | MR | Zbl

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