Local well-posedness and stability of peakons for a generalized Dullin–Gottwald–Holm equation

2011 ◽  
Vol 74 (7) ◽  
pp. 2497-2507 ◽  
Author(s):  
Xingxing Liu ◽  
Zhaoyang Yin
Keyword(s):  
Well Posedness ◽  
Holm Equation

scholarly journals Local well-posedness of the Camassa-Holm equation on the real line

2017 ◽  
Vol 37 (6) ◽  
pp. 3285-3299
Author(s):  
Jae Min Lee ◽  
◽  
Stephen C. Preston ◽  
Keyword(s):  
Real Line ◽  
Well Posedness ◽  
The Real ◽  
Holm Equation

scholarly journals On the Blow-Up of Solutions of a Weakly Dissipative Modified Two-Component Periodic Camassa-Holm System

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Yongsheng Mi ◽  
Chunlai Mu ◽  
Weian Tao
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Strong Solutions ◽  
Well Posedness ◽  
Holm Equation ◽  
Two Component ◽  
The Cauchy Problem ◽  
Blow Up Rate

We study the Cauchy problem of a weakly dissipative modified two-component periodic Camassa-Holm equation. We first establish the local well-posedness result. Then we derive the precise blow-up scenario and the blow-up rate for strong solutions to the system. Finally, we present two blow-up results for strong solutions to the system.

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

2014 ◽  
Vol 12 ◽  
pp. 10-20
Author(s):  
Jiang Bo Zhou ◽  
Jun De Chen ◽  
Wen Bing Zhang
Keyword(s):  
Global Existence ◽  
Shallow Water ◽  
Blow Up ◽  
Shallow Water Equation ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Holm Equation ◽  
Special Cases ◽  
Long Time

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.

scholarly journals The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Nan Li ◽  
Shaoyong Lai ◽  
Shuang Li ◽  
Meng Wu
Keyword(s):  
Sobolev Space ◽  
Existence Of Solutions ◽  
Well Posedness ◽  
Unique Global Solution ◽  
Initial Value ◽  
Regularization Technique ◽  
Global Existence Of Solutions ◽  
Holm Equation ◽  
Sign Condition ◽  
Nonlinear Generalization

A nonlinear generalization of the Camassa-Holm equation is investigated. By making use of the pseudoparabolic regularization technique, its local well posedness in Sobolev spaceHS(R)withs>3/2is established via a limiting procedure. Provided that the initial valueu0satisfies the sign condition andu0∈Hs(R)  (s>3/2), it is shown that there exists a unique global solution for the equation in spaceC([0,∞);Hs(R))∩C1([0,∞);Hs−1(R)).

Well-posedness and blow-up solution for the stochastic Dullin-Gottwald-Holm equation

2019 ◽  
Vol 60 (8) ◽  
pp. 083513 ◽  
Author(s):  
Wujun Lv ◽  
Ping He ◽  
Qinghua Wang
Keyword(s):  
Blow Up ◽  
Well Posedness ◽  
Holm Equation
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