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Blow-Up Phenomena and Global Existence to a Weakly Dissipative Shallow Water Equation

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Abstract:

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.

Info:

Periodical:
The Bulletin of Society for Mathematical Services and Standards (Volume 12)
Pages:
10-20
DOI:
10.18052/www.scipress.com/BSMaSS.12.10
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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