Global Existence and Long-Time Behavior of Solutions to the Vlasov–Poisson–Fokker–Planck System

2020 ◽  
Vol 170 (1) ◽  
pp. 853-881
Author(s):  
Xiaolong Wang
Author(s):  
Jiang Bo Zhou ◽  
Jun De Chen ◽  
Wen Bing Zhang

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.


2004 ◽  
Vol 141 (3) ◽  
pp. 237-257 ◽  
Author(s):  
C. Sparber ◽  
J. A. Carrillo ◽  
P. A. Markowich ◽  
J. Dolbeault

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