Asymptotic Stability of Shock Profiles and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Viscous Conservation Laws
文献类型：期刊论文
| 作者 | Xin, Zhouping1,2; Yuan, Qian3 ; Yuan, Yuan4
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| 刊名 | INDIANA UNIVERSITY MATHEMATICS JOURNAL
 |
| 出版日期 | 2021 |
| 卷号 | 70期号:6页码:2295-2349 |
| ISSN号 | 0022-2518 |
| 英文摘要 | This paper studies the asymptotic stability of shock profiles and rarefaction waves under space-periodic perturbations for one-dimensional convex scalar viscous conservation laws. For the shock profile, we show that the solution approaches the background shock profile with a constant shift in the L-infinity (R) norm at exponential rates. The new phenomena contrasting to the case of localized perturbations is that the constant shift cannot be determined by the initial excessive mass in general, which indicates that the periodic oscillations at infinities make contributions to this shift. And the vanishing viscosity limit for the shift is also shown. The key elements of the proof consist of the construction of an ansatz which carries periodic oscillations of the solution as vertical bar X vertical bar -> +infinity, the anti-derivative variable argument, and an elaborate use of the maximum principle. For the rarefaction wave, we also show the stability in the L-infinity (R) norm. |
| 资助项目 | Zheng Ge Ru Foundation through Hong Kong RGC Earmarked Research Grants[CUHK-14300917] ; Zheng Ge Ru Foundation through Hong Kong RGC Earmarked Research Grants[CUHK-14305315] ; Zheng Ge Ru Foundation through Hong Kong RGC Earmarked Research Grants[CUHK-14300819] ; Zheng Ge Ru Foundation through Hong Kong RGC Earmarked Research Grants[CUHK-14302819] ; Zheng Ge Ru Foundation through Hong Kong RGC Earmarked Research Grants[CUHK-14302917] ; Guangdong Province Basic and Applied Basic Research Foundation[2020B1515310002] ; China Postdoctoral Science Founda-tion[2019M660831] ; China Postdoctoral Science Founda-tion[2020TQ0345] ; Natural Science Founda-tion of China[11901208] ; Natural Science Founda-tion of China[11971009] ; Natural Science Foun-dation of Guangdong Province[2021A1515010247] ; National Key Research and Development Program of China[2021YFA1002900] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| 出版者 | INDIANA UNIV MATH JOURNAL |
| WOS记录号 | WOS:000733338700003 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59802]  |
| 专题 | 博士后 |
| 通讯作者 | Yuan, Qian |
| 作者单位 | 1.Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China 2.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing, Peoples R China 4.South China Normal Univ, Sch Math Sci, Guangzhou, Guangdong, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xin, Zhouping,Yuan, Qian,Yuan, Yuan. Asymptotic Stability of Shock Profiles and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Viscous Conservation Laws[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL,2021,70(6):2295-2349. |
| APA | Xin, Zhouping,Yuan, Qian,&Yuan, Yuan.(2021).Asymptotic Stability of Shock Profiles and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Viscous Conservation Laws.INDIANA UNIVERSITY MATHEMATICS JOURNAL,70(6),2295-2349. |
| MLA | Xin, Zhouping,et al."Asymptotic Stability of Shock Profiles and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Viscous Conservation Laws".INDIANA UNIVERSITY MATHEMATICS JOURNAL 70.6(2021):2295-2349. |
入库方式： OAI收割
来源：数学与系统科学研究院
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