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

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.

Keywords

• Local solvability
• blow-up
• Benjamin-Bona-Mahony-Burgers
• Rosenau-Burgers
• Korteweg-de Vries-Benjamin-Bona-Mahony