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Abstract
Considered herein is the well-posedness of a periodic Degasperis–Procesi equation with linear dispersion modeling for an approximation to the incompressible Euler equation for shallow water waves. The existence of permanent waves is established with certain small initial profiles depending on the linear dispersive parameter in a range of Sobolev spaces. On the other hand, sufficient conditions guaranteeing the development of breaking waves in finite time are established. Moreover, the blow-up rate of breaking waves is obtained.
Received: 2009-04-20
Revised: 2010-05-01
Published Online: 2011-03-28
Published in Print: 2011-August
© Walter de Gruyter Berlin · New York 2011