Local Well-Posedness for a Generalized Integrable Shallow Water Equation with Strong Dispersive Term

2021 ◽  
Vol 15 (4) ◽  
pp. 429-436
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Well Posedness ◽  
Dispersive Term

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 dynamic properties of solutions for a nonlinear shallow water equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yeqin Su ◽  
Shaoyong Lai ◽  
Sen Ming
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Shallow Water ◽  
Wave Breaking ◽  
Dynamic Properties ◽  
Shallow Water Equation ◽  
Propagation Speed ◽  
Well Posedness ◽  
The Cauchy Problem ◽  
Infinite Propagation Speed

Abstract The local well-posedness for the Cauchy problem of a nonlinear shallow water equation is established. The wave-breaking mechanisms, global existence, and infinite propagation speed of solutions to the equation are derived under certain assumptions. In addition, the effects of coefficients λ, β, a, b, and index k in the equation are illustrated.

scholarly journals Well-posedness and blow-up phenomena for a higher order shallow water equation

2011 ◽  
Vol 251 (12) ◽  
pp. 3488-3499 ◽  
Author(s):  
Chunlai Mu ◽  
Shouming Zhou ◽  
Rong Zeng
Keyword(s):  
Shallow Water ◽  
Blow Up ◽  
Shallow Water Equation ◽  
Higher Order ◽  
Well Posedness

scholarly journals Well-posedness of a highly nonlinear shallow water equation on the circle

2020 ◽  
Vol 197 ◽  
pp. 111849
Author(s):  
Nilay Duruk Mutlubas ◽  
Anna Geyer ◽  
Ronald Quirchmayr
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Well Posedness ◽  
Highly Nonlinear
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