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

© 2011 Russian Academy of Sciences, (DoM) and London Mathematical Society, Turpion Ltd
, , Citation Anatoly I Aristov 2011 Izv. Math. 75 871 DOI 10.1070/IM2011v075n05ABEH002556

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Dates

  1. Received 26 January 2009
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1064-5632/75/5/871

Abstract

We investigate the asymptotic behaviour as  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.

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