We first establish the local well-posedness for a weakly dissipative shallow water equation which includes both the weakly dissipative Camassa-Holm equation and the weakly dissipative Degasperis-Procesi equation as its special cases. Then two blow-up results are derived for certain initial profiles. Finally, We study the long time behavior of the solutions.

Periodical:

The Bulletin of Society for Mathematical Services and Standards (Volume 12)

Pages:

10-20

Citation:

J. B. Zhou et al., "Blow-Up Phenomena and Global Existence to a Weakly Dissipative Shallow Water Equation", The Bulletin of Society for Mathematical Services and Standards, Vol. 12, pp. 10-20, 2014

Online since:

Dec 2014

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Open Access

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Creative Commons Attribution 4.0 International License

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