scholarly journals Global existence and long-time behavior of entropy weak solutions to a quasilinear hyperbolic blood flow model

2011 ◽  
Vol 6 (4) ◽  
pp. 625-646 ◽  
Author(s):  
Tong Li ◽  
◽  
Kun Zhao ◽  
Keyword(s):  
Blood Flow ◽  
Global Existence ◽  
Weak Solutions ◽  
Flow Model ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time ◽  
Blood Flow Model

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 Solutions to a model with Neumann boundary conditions for sea-ice growth

2021 ◽  
Author(s):  
Yangxin Tang ◽  
Lin Zheng
Keyword(s):  
Global Existence ◽  
Sea Ice ◽  
Boundary Conditions ◽  
Weak Solutions ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Dirichlet Boundary Conditions ◽  
Time Behavior ◽  
Ice Growth ◽  
Long Time

We continue to study an initial boundary value problems to a model describing the evolution in time of diffusive phase interfaces in sea-ice growth. In a previous paper global existence and the long-time of behavior of weak solutions in one space was studied under Dirichlet boundary conditions. Here we show that the global existence of weak solutions and the long-time behavior are also studied under Neumann boundary condition. In this paper we study in space dimension lower than or equal to $3$.

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