Asymptotic expansion of solutions to the periodic problem for a~non-linear Sobolev-type equation

E. I. Kaikina; P. I. Naumkin; I. A. Shishmarev

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Asymptotic expansion of solutions to the periodic problem for a~non-linear Sobolev-type equation

E. I. Kaikina ; P. I. Naumkin ; I. A. Shishmarev

Izvestiya. Mathematics , Tome 77 (2013) no. 2, pp. 313-324

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

Résumé

We study the long-time behaviour of solutions to the periodic problem for a non-linear Sobolev-type equation. In the case of non-small initial perturbations we get estimates for the decay as a function of time. In the case of small initial data we prove an asymptotic formula for solutions to the periodic problem for a non-linear Sobolev-type equation.

Keywords: periodic problem, asymptotic behaviour.
Mots-clés : Sobolev-type equations

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     author = {E. I. Kaikina and P. I. Naumkin and I. A. Shishmarev},
     title = {Asymptotic expansion of solutions to the periodic problem for a~non-linear {Sobolev-type} equation},
     journal = {Izvestiya. Mathematics },
     pages = {313--324},
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     volume = {77},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2013_77_2_a3/}
}

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E. I. Kaikina; P. I. Naumkin; I. A. Shishmarev. Asymptotic expansion of solutions to the periodic problem for a~non-linear Sobolev-type equation. Izvestiya. Mathematics , Tome 77 (2013) no. 2, pp. 313-324. http://geodesic.mathdoc.fr/item/IM2_2013_77_2_a3/