Geodesic
On the Cauchy problem for a~Sobolev-type equation with quadratic non-linearity
Izvestiya. Mathematics , Tome 75 (2011) no. 5, pp. 871-887

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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, asymptotic behaviour of solutions, perturbation theory.
Mots-clés : Sobolev-type equations 
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     author = {A. I. Aristov},
     title = {On the {Cauchy} problem for {a~Sobolev-type} equation with quadratic non-linearity},
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A. I. Aristov. On the Cauchy problem for a~Sobolev-type equation with quadratic non-linearity. Izvestiya. Mathematics , Tome 75 (2011) no. 5, pp. 871-887. http://geodesic.mathdoc.fr/item/IM2_2011_75_5_a0/