scholarly journals On the Long-Time Asymptotic Behavior of the Modified Korteweg--de Vries Equation with Step-like Initial Data

2020 ◽  
Vol 52 (6) ◽  
pp. 5892-5993
Author(s):  
Tamara Grava ◽  
Alexander Minakov
Keyword(s):  
Asymptotic Behavior ◽  
Initial Data ◽  
Vries Equation ◽  
De Vries ◽  
Long Time ◽  
Time Asymptotic Behavior

scholarly journals Long-time asymptotic behavior for an extended modified Korteweg-de Vries equation

2019 ◽  
Vol 17 (7) ◽  
pp. 1877-1913
Author(s):  
Nan Liu ◽  
Boling Guo ◽  
Dengshan Wang ◽  
Yufeng Wang
Keyword(s):  
Asymptotic Behavior ◽  
Vries Equation ◽  
De Vries ◽  
Long Time ◽  
Time Asymptotic Behavior

scholarly journals Long-time asymptotics for the Korteweg–de Vries equation with step-like initial data

Nonlinearity ◽  
2013 ◽  
Vol 26 (7) ◽  
pp. 1839-1864 ◽  
Author(s):  
Iryna Egorova ◽  
Zoya Gladka ◽  
Volodymyr Kotlyarov ◽  
Gerald Teschl
Keyword(s):  
Initial Data ◽  
Vries Equation ◽  
Time Asymptotics ◽  
De Vries ◽  
Long Time ◽  
Long Time Asymptotics

scholarly journals On long-time asymptotic behavior for solutions to 2D temperature-dependent tropical climate model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Chaoying Li ◽  
Xiaojing Xu ◽  
Zhuan Ye
Keyword(s):  
Asymptotic Behavior ◽  
Initial Data ◽  
Climate Model ◽  
Tropical Climate ◽  
Two Dimensional ◽  
Temperature Dependent ◽  
General Initial Data ◽  
Long Time ◽  
Tropical Climate Model ◽  
Time Asymptotic Behavior

<p style='text-indent:20px;'>In this paper, we are concerned with the long-time asymptotic behavior of the two-dimensional temperature-dependent tropical climate model. More precisely, we obtain the sharp time-decay of the solution of the system with the general initial data belonging to an appropriate Sobolev space with negative indices. In addition, when such condition of the initial data is absent, it is shown that any spatial derivative of the positive integer <inline-formula><tex-math id="M1">\begin{document}$ k $\end{document}</tex-math></inline-formula>-order of the solution actually decays at least at the rate of <inline-formula><tex-math id="M2">\begin{document}$ (1+t)^{-\frac{k}{2}} $\end{document}</tex-math></inline-formula>.</p>

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