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Existence of permanent and breaking waves for the periodic Degasperis–Procesi equation with linear dispersion
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Published/Copyright:
March 28, 2011
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
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Articles in the same Issue
- Coefficients and non-triviality of the Jones polynomial
- Distribution of algebraic numbers
- Some local-global non-vanishing results of theta lifts for symplectic-orthogonal dual pairs
- Characterizing quaternion rings over an arbitrary base
- Transcendence in positive characteristic and special values of hypergeometric functions
- Factoring 3-fold flips and divisorial contractions to curves
- Existence of permanent and breaking waves for the periodic Degasperis–Procesi equation with linear dispersion
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