Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 69, pp. 1-16.

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

Authors: Maxim O. Korpusov (Lomonosov Moscow State Univ., Moscow, Russia)
         Egor V. Yushkov   (Lomonosov Moscow State Univ., Moscow, Russia)

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.