Theoretical and numerical studies on global stability of traveling waves with oscillations for time-delayed nonlocal dispersion equations
Theoretical and numerical studies on global stability of traveling waves with oscillations for time-delayed nonlocal dispersion equations
复制标题
时滞非局域色散方程带振荡行波整体稳定性的理论与数值研究
DOI：
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发表时间：
2018-10
影响因子：
1.1
通讯作者：
Yin Jingxue
中科院分区：
文献类型：
--
作者：
Xu Tianyuan;Ji Shanming;Huang Rui;Mei Ming;Yin Jingxue
本文关注具有时滞的非局部色散方程的含振荡的非临界/临界行波的全局稳定性。我们首先从理论上证明所有行波，尤其是临界振荡行波……
This paper is concerned with the global stability of non-critical/critical traveling waves with oscillations for time-delayed nonlocal dispersion equations. We first theoretically prove that all traveling waves, especially the critical oscillatory traveling waves, are globally stable in a certain weighted space, where the convergence rates to the non-critical oscillatory traveling waves are time-exponential, and the convergence to the critical oscillatory traveling waves are time-algebraic. Both of the rates are optimal. The approach adopted is the weighted energy method with the fundamental solution theory for time-delayed equations. Secondly, we carry out numerical computations in different cases, which also confirm our theoretical results. Because of oscillations of the solutions and nonlocality of the equation, the numerical results obtained by the regular finite difference scheme are not stable, even worse to be blow-up. In order to overcome these obstacles, we propose a new finite difference scheme by adding artificial viscosities to both sides of the equation, and obtain the desired numerical results.
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DOI：
10.1137/090776342
发表时间：
2010-11
期刊：
SIAM J. Math. Anal.
影响因子：
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作者：
Ming Mei;Chunhua Ou;Xiao-Qiang Zhao
通讯作者：
Ming Mei;Chunhua Ou;Xiao-Qiang Zhao
影响因子：
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作者：
D. Khusainov;A. Ivanov;I. V. Kovarzh
通讯作者：
D. Khusainov;A. Ivanov;I. V. Kovarzh
DOI：
10.1007/978-3-662-05281-5_3
发表时间：
2003
期刊：
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影响因子：
--
作者：
P. Fife
通讯作者：
P. Fife
DOI：
10.1090/surv/165
发表时间：
2010-10
期刊：
--
影响因子：
--
作者：
F. Andreu-Vaillo;J. Mazón;J. Rossi;J. J. Toledo-Melero-J.
通讯作者：
F. Andreu-Vaillo;J. Mazón;J. Rossi;J. J. Toledo-Melero-J.
影响因子：
1.1
作者：
X. Xing;Yaping Wu
通讯作者：
X. Xing;Yaping Wu