Global conservative solutions of the Dullin-Gottwald-Holm equation

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September 2007, 19(3): 575-594. doi: 10.3934/dcds.2007.19.575

Global conservative solutions of the Dullin-Gottwald-Holm equation

1.	Faculty of Mathematics, D.A.L., University of Craiova, Romania

Received April 2007 Revised June 2007 Published July 2007

Abstract
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A new approach to the analysis of wave-breaking solutions to the Dullin-Gottwald-Holm equation is presented in this paper. Introduction of a set of variables allows for solving the singularities. A continuous semigroup of solutions is also built. The solutions have constant $H^{1}$-energy for almost every time with respect to the Lebesgue measure.

Keywords: Global conservative solution, nonlocal conservation law..

Mathematics Subject Classification: Primary: 35Q35, 35Q7.

Citation: Octavian G. Mustafa. Global conservative solutions of the Dullin-Gottwald-Holm equation. Discrete & Continuous Dynamical Systems - A, 2007, 19 (3) : 575-594. doi: 10.3934/dcds.2007.19.575

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