scholarly journals Global existence and long-time behavior of smooth solutions of two-fluid Euler–Maxwell equations

2012 ◽  
Vol 29 (5) ◽  
pp. 737-759 ◽  
Author(s):  
Yue-Jun Peng
Keyword(s):  
Global Existence ◽  
Maxwell Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Smooth Solutions ◽  
Long Time ◽  
Two Fluid

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.

GLOBAL EXISTENCE AND LONG-TIME BEHAVIOR FOR A PARTIALLY DISSIPATIVE SYSTEM MODELLING A POLYMERIZATION–CRYSTALLIZATION REACTION

1998 ◽  
Vol 08 (02) ◽  
pp. 219-249 ◽  
Author(s):  
SERGE NJAMKEPO
Keyword(s):  
Global Existence ◽  
Unbounded Domain ◽  
Dissipative System ◽  
Exponential Attractor ◽  
System Modelling ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Bounded Interval ◽  
Crystallization Reaction ◽  
Long Time

We consider a partially dissipative system in a bounded interval of ℝ and we prove the existence of a local exponential attractor. The key tool is the adaptation of a method due to Babin and Nicolaenko, for a dissipative system in an unbounded domain.

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