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