Electron. J. Diff. Equ., Vol. 2014 (2014), No. 69, pp. 1-16.

Local solvability and blow-up for Benjamin-Bona-Mahony-Burgers, Rosenau-Burgers and Korteweg-de Vries-Benjamin-Bona-Mahony equations

Maxim O. Korpusov, Egor V. Yushkov

Abstract:
In this article some well-known problems in mathematical physics for Benjamin-Bona-Mahony-Burgers, Rosenau-Burgers and Korteweg-de Vries-Benjamin-Bona-Mahony equations are considered. These equations describe important processes in different fields of physics, particulary in hydro- and electrodynamics. We study initial-boundary problems with natural physical boundary conditions. Sufficient conditions of local solvability and blow-up in finite time are obtained. For this the methods of contraction mapping and nonlinear capacity, developed by Galaktionov, Pokhozhaev and Mitidieri, are used.

Submitted August 6, 2013. Published March 15, 2014.
Math Subject Classifications: 35B44.
Key Words: Local solvability; blow-up; Benjamin-Bona-Mahony-Burgers; Rosenau-Burgers; Korteweg-de Vries-Benjamin-Bona-Mahony.

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Maxim O. Korpusov
Chair of Mathematics, Physics Faculty
M. V. Lomonosov Moscow State University
Moscow, Russia
email: korpusov@gmail.com
Egor V. Yushkov
Chair of Mathematics, Physics Faculty
M. V. Lomonosov Moscow State University
Moscow, Russia
email: yushkov.msu@mail.ru

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