Global existence and large time behavior of solutions for the bipolar quantum hydrodynamic models in the quarter plane

2013 ◽  
Vol 36 (11) ◽  
pp. 1409-1422 ◽  
Author(s):  
Yeping Li
Keyword(s):  
Global Existence ◽  
Large Time ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Hydrodynamic Models ◽  
Quarter Plane ◽  
Quantum Hydrodynamic

Asymptotics of solutions to a fifth-order modified Korteweg–de Vries equation in the quarter plane

2020 ◽  
pp. 1-46
Author(s):  
Nan Liu ◽  
Boling Guo
Keyword(s):  
Large Time ◽  
Vries Equation ◽  
Large Time Behavior ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Time Behavior ◽  
Transform Method ◽  
Quarter Plane ◽  
De Vries ◽  
Fifth Order

The large-time behavior of solutions to a fifth-order modified Korteweg–de Vries equation in the quarter plane is established. Our approach uses the unified transform method of Fokas and the nonlinear steepest descent method of Deift and Zhou.

scholarly journals Asymptotic Behavior of Solutions to Fast Diffusive Non-Newtonian Filtration Equations Coupled by Nonlinear Boundary Sources

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Wang Zejia ◽  
Wang Shunti ◽  
Zhang Chengbin
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Nonlinear Boundary ◽  
Large Time ◽  
Large Time Behavior ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Multidimensional Problem ◽  
Critical Curves

This paper is concerning the asymptotic behavior of solutions to the fast diffusive non-Newtonian filtration equations coupled by the nonlinear boundary sources. We are interested in the critical global existence curve and the critical Fujita curve, which are used to describe the large-time behavior of solutions. It is shown that the above two critical curves are both the same for the multidimensional problem we considered.

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