Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Daria Bolbot, D. Mitsotakis, A. Tzavaras
{"title":"Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics","authors":"Daria Bolbot, D. Mitsotakis, A. Tzavaras","doi":"10.1090/qam/1658","DOIUrl":null,"url":null,"abstract":"The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence of traveling waves to shocks. The problem is recast as a Hamiltonian system with small friction, and an analysis of the length of oscillations yields convergence in the moderate dispersion regime \n\n \n \n ε\n ,\n δ\n →\n 0\n \n \\varepsilon , \\delta \\to 0\n \n\n with \n\n \n \n δ\n =\n o\n (\n ε\n )\n \n \\delta = o(\\varepsilon )\n \n\n, under hypotheses that the limiting shock is admissible according to the Liu E-condition and is not a contact discontinuity at either end state. A similar convergence result is proved for traveling waves of the quantum hydrodynamic system with artificial viscosity as well as for a viscous Peregrine-Boussinesq system where traveling waves model undular bores, in all cases in the moderate dispersion regime.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quarterly of Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/qam/1658","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1

Abstract

The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence of traveling waves to shocks. The problem is recast as a Hamiltonian system with small friction, and an analysis of the length of oscillations yields convergence in the moderate dispersion regime ε , δ → 0 \varepsilon , \delta \to 0 with δ = o ( ε ) \delta = o(\varepsilon ) , under hypotheses that the limiting shock is admissible according to the Liu E-condition and is not a contact discontinuity at either end state. A similar convergence result is proved for traveling waves of the quantum hydrodynamic system with artificial viscosity as well as for a viscous Peregrine-Boussinesq system where traveling waves model undular bores, in all cases in the moderate dispersion regime.
弹性力学和量子流体力学扩散散射近似中的散射激波
其目的是评估中等分散状态下扩散和分散对冲击的综合影响。对于一维弹性(或p-系统)方程的扩散色散近似,我们研究了行波对冲击的收敛性。该问题被重新定义为具有小摩擦的哈密顿系统,并且对振荡长度的分析产生了在中等色散区ε,δ的收敛性→ 0\varepsilon,\ delta \ to 0,δ=o(ε)\ delta=o(\ varepsilo),假设极限冲击根据Liu E条件是可容许的,并且在任何末端状态都不是接触不连续性。对于具有人工粘性的量子流体动力学系统的行波以及粘性Peregrine-Boussinesq系统,证明了类似的收敛结果,其中行波在所有情况下都模拟了中等色散状态下的非圆形孔。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Quarterly of Applied Mathematics
Quarterly of Applied Mathematics 数学-应用数学
CiteScore
1.90
自引率
12.50%
发文量
31
审稿时长
>12 weeks
期刊介绍: The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信