This article is cited in 1 paper

Periodic solutions of the Hopf equation

A. B. Shabat<sup>ab

a</sup> Landau Institute for Theoretical Physics, RAS, Moscow, Russia
^b Aliev Karachaev-Cherkess State University, Karachaevsk, Russia

Abstract: We consider the long-time dynamics of approximate solutions of the boundary-value problem for the Hopf equation on a finite segment. Together with the initial conditions, for instance, we impose the zero Dirichlet conditions on both ends of the segment. In this case, all features of solutions associated with the intersections of characteristics are accumulated on a strip bounded by the vertical characteristics emitted from the boundary points.

Keywords: generalized solution, conservation law, Galerkin method.

Received: 12.05.2013

DOI: 10.4213/tmf8546

 English version: Theoretical and Mathematical Physics, 2013, 177:2, 1471–1478

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