E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Periodic Boundary Value Problem for Nonlinear Sobolev-Type Equations”, Funktsional. Anal. i Prilozhen., 2010, Volume 44, Issue 3,Pages <nobr>14

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Periodic Boundary Value Problem for Nonlinear Sobolev-Type Equations

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

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

Abstract: The large-time asymptotic behavior of solutions to the periodic boundary value problem for a nonlinear Sobolev-type equation is studied. In particular, the case where the initial perturbations are not small is considered. In this case, the large-time behavior of solutions is dichotomous.

Keywords: periodic boundary value problem, Sobolev-type equation, asymptotic behavior.

UDC: 517.9+535.5

Received: 20.04.2009

DOI: 10.4213/faa2993