KdV-type equation limit for ion dynamics system

Rong Rong; Yi Peng

doi:10.3934/cpaa.2021037

Article Contents

2021, Volume 20, Issue 4: 1699-1719. Doi: 10.3934/cpaa.2021037

This issue Previous Article The regularity lifting methods for nonnegative solutions of Lane-Emden system Next Article Extremal functions for a class of trace Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary

KdV-type equation limit for ion dynamics system

Rong Rong^1, , and
Yi Peng^2,

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China
2.
School of Mathematics and Statistics, Chongqing University, Chongqing, 400044, China

^* Corresponding author
^* Corresponding author

Received: June 30, 2020

Revised: December 31, 2020

Early access: March 2021

Published: April 2021

The first author (Rong Rong) was supported by the Innovation Research for the Postgraduates of Guangzhou University under Grant (2020GDJC-D09)

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Abstract

In this paper, we consider the KdV-type limit for ion dynamics system. Under the Gardner-Morikawa type transforms, we derive the KdV-type equation by the scaling $ \varepsilon^{\frac{1}{4}}(x-t) \rightarrow X $, $ \varepsilon^{\frac{3}{4}}t\rightarrow T $ for ion dynamics system in one dimension. By proving the uniform estimates for the remainders system, we show that when $ \varepsilon \rightarrow 0 $, the solutions to the ion dynamics system converge globally in time to the solutions of the KdV-type equation.

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Mathematics Subject Classification: Primary: 35Q35.

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