This article is cited in 2 papers

On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity

A. I. Aristov


Abstract: We investigate the asymptotic behaviour as $t\to\infty$ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.

Keywords: non-linear partial differential equations, Sobolev-type equations, asymptotic behaviour of solutions, perturbation theory.

UDC: 517.955.8

MSC: Primary 35C20; Secondary 35K60, 76B15

Received: 26.01.2009
Revised: 05.05.2010

DOI: 10.4213/im4079

 English version: Izvestiya: Mathematics, 2011, 75:5, 871–887

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