Geodesic
Asymptotic behaviour of solutions of
Sbornik. Mathematics, Tome 199 (2008) no. 4, pp. 539-556

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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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     author = {Yu. V. Egorov and V. A. Kondratiev},
     title = {Asymptotic behaviour of solutions of},
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     url = {http://geodesic.mathdoc.fr/item/SM_2008_199_4_a3/}
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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/