一个弱耗散修正的二分量Dullin-Gottwald-Holm系统解的行为研究

数学物理学报 ›› 2020, Vol. 40 ›› Issue (5): 1204-1223.

一个弱耗散修正的二分量Dullin-Gottwald-Holm系统解的行为研究

田守富()

^{中国矿业大学数学学院江苏徐州 221116}

收稿日期:2018-03-05 出版日期:2020-10-26 发布日期:2020-11-04
作者简介:田守富, E-mail:sftian@cumt.edu.cn, shoufu2006@126.com
基金资助:
国家自然科学基金(11975306);江苏省自然科学基金(BK20181351);江苏省"六大人才高峰"基金(JY-059)

On the Behavior of the Solution of a Weakly Dissipative Modified Two-Component Dullin-Gottwald-Holm System

Shoufu Tian()

^{School of Mathematics, China University of Mining and Technology, Jiangsu Xuzhou 221116}

Received:2018-03-05 Online:2020-10-26 Published:2020-11-04
Supported by:
the NSFC(11975306);the NSF of Jiangsu Province(BK20181351);the Six Talent Peaks Project in Jiangsu Province(JY-059)

摘要/Abstract

摘要：

该文研究了弱耗散修正二分量Dullin-Gottwald-Holm（mDGH2）系统的柯西问题.分析了局部的适定性和全局的存在性，证明了在条件$\left(\|y_{0}\|_{L^{2}}^{2}+\|\rho_{0}\|^{2}_{L^{2}}\right)^{\frac{1}{2}}<\frac{4\lambda} {3}$下不会发生爆破现象.此外还推导出了精确的爆破方案，并给出了几个保证弱耗散mDGH2系统解的爆破准则.所得的结果表明弱耗散项不影响弱耗散mDGH2系统的解.

关键词: 二分量peakon系统, 弱耗散, 爆破

Abstract:

In this paper, we consider the Cauchy problem of a weakly dissipative modified two-component Dullin-Gottwald-Holm (mDGH2) system. The local well-posedness and the global existence are analyzed, which is to prove that blow-up phenomena cannot happen under the condition $\left(\|y_{0}\|_{L^{2}}^{2}+\|\rho_{0}\|^{2}_{L^{2}}\right)^{\frac{1}{2}}<\frac{4\lambda} {3}.$ We derive the precise blow-up scenario, and then provide several criteria guaranteeing the blow-up of the solutions to the weakly dissipative mDGH2 system. It is worth noting that the solution to the weakly dissipative system is not affected by the weakly dissipative term.

Key words: Two-component peakon system, Weakly dissipative, Blow-up

中图分类号:

O175.2

田守富. 一个弱耗散修正的二分量Dullin-Gottwald-Holm系统解的行为研究[J]. 数学物理学报, 2020, 40(5): 1204-1223.

Shoufu Tian. On the Behavior of the Solution of a Weakly Dissipative Modified Two-Component Dullin-Gottwald-Holm System[J]. Acta mathematica scientia,Series A, 2020, 40(5): 1204-1223.

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