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Wave-breaking phenomena, decay properties and limit behaviour of solutions of the Degasperis—Procesi equation

Published online by Cambridge University Press:  10 August 2012

Fei Guo
Fei Guo
Affiliation:
School of Mathematical Sciences and Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210046, People's Republic of China (guof@njnu.edu.cn)
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Abstract

We investigate some properties of solutions of the Degasperis–Procesi equation, which is an approximation to the incompressible Euler equation in shallow water theory. Sufficient conditions for wave breaking are found both on an infinite line and in a periodic domain by the method of characteristics. Moreover, we show that the solution enjoys the same decay property as the initial data. Finally, the weak and strong limits, respectively, of the solution as the dispersive parameter goes to zero are investigated.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 4 , August 2012 , pp. 805 - 824
Copyright
Copyright © Royal Society of Edinburgh 2012

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