October  2010, 26(4): 1269-1290. doi: 10.3934/dcds.2010.26.1269

On the initial-value problem to the Degasperis-Procesi equation with linear dispersion

1. 

School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210046, China

2. 

Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539, United States

3. 

Jiangsu Provincial Key Laboratory for NSLSCS, School of Mathematics, Nanjing Normal University, Nanjing, Jiangsu, 210046, China

4. 

Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408

Received  February 2009 Revised  March 2009 Published  December 2009

In this paper, we consider the initial-value problem for the Degasperis-Procesi equation with a linear dispersion, which is an approximation to the incompressible Euler equation for shallow water waves. We establish local well-posedness and some global existence of solutions for certain initial profiles and determine the wave breaking phenomena for the equation. Finally, we verify the occurrence of the breaking waves by numerical simulations.
Citation: Fei Guo, Bao-Feng Feng, Hongjun Gao, Yue Liu. On the initial-value problem to the Degasperis-Procesi equation with linear dispersion. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1269-1290. doi: 10.3934/dcds.2010.26.1269
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