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

摘要

We investigate the asymptotic behaviour as t → ∞ 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.