L-2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws | |
Kang, Moon-Jin3,4; Vasseur, Alexis F.1; Wang, Yi2,5![]() | |
刊名 | JOURNAL OF DIFFERENTIAL EQUATIONS
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2019-08-15 | |
卷号 | 267期号:5页码:2737-2791 |
ISSN号 | 0022-0396 |
DOI | 10.1016/j.jde.2019.03.030 |
英文摘要 | We consider a L-2-contraction (a L-2-type stability) of large viscous shock waves for the multidimensional scalar viscous conservation laws, up to a suitable shift by using the relative entropy methods. Quite different from the previous results, we find a new way to determine the shift function, which depends both on the time and space variables and solves a viscous Hamilton-Jacobi type equation with source terms. Moreover, we do not impose any conditions on the anti-derivative variables of the perturbation around the shock profile. More precisely, it is proved that if the initial perturbation around the viscous shock wave is suitably small in L-2-norm, then the L-2-contraction holds true for the viscous shock wave up to a suitable shift function. Note that BY-norm or the L-infinity-norm of the initial perturbation and the shock wave strength can be arbitrarily large. Furthermore, as the time t tends to infinity, the L-2-contraction holds true up to a (spatially homogeneous) time-dependent shift function. In particular, if we choose some special initial perturbations, then L-2-convergence of the solutions towards the associated shock profile can be proved up to a time-dependent shift. (C) 2019 Elsevier Inc. All rights reserved. |
资助项目 | Basic Science Research Program through the National Research Foundation of Korea[NRF-2017R1C1B5076510] ; NSF[DMS 1614918] ; National Natural Sciences Foundation of China[11671385] ; National Natural Sciences Foundation of China[11688101] ; CAS Interdisciplinary Innovation Team |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
WOS记录号 | WOS:000468614700002 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/34748] ![]() |
专题 | 应用数学研究所 |
通讯作者 | Wang, Yi |
作者单位 | 1.Univ Texas Austin, Dept Math, Austin, TX 78712 USA 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Sookmyung Womens Univ, Dept Math, Seoul 04310, South Korea 4.Sookmyung Womens Univ, Res Inst Nat Sci, Seoul 04310, South Korea 5.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China |
推荐引用方式 GB/T 7714 | Kang, Moon-Jin,Vasseur, Alexis F.,Wang, Yi. L-2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2019,267(5):2737-2791. |
APA | Kang, Moon-Jin,Vasseur, Alexis F.,&Wang, Yi.(2019).L-2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws.JOURNAL OF DIFFERENTIAL EQUATIONS,267(5),2737-2791. |
MLA | Kang, Moon-Jin,et al."L-2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws".JOURNAL OF DIFFERENTIAL EQUATIONS 267.5(2019):2737-2791. |
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