E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Asymptotic expansion of solutions to the periodic problem for a non-linear Sobolev-type equation”, Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 2,Pages <nobr>97

This article is cited in 4 papers

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

E. I. Kaikina^a, P. I. Naumkin^a, I. A. Shishmarev^b

^a National Autonomous University of Mexico, Institute of Mathematics
^b M. V. Lomonosov Moscow State University

Abstract: 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: Sobolev-type equations, periodic problem, asymptotic behaviour.

UDC: 517.956.8+517.953

MSC: 35B40, 35K61

Received: 17.01.2012

DOI: 10.4213/im7957