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L-2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws
Kang, Moon-Jin1,2; Vasseur, Alexis F.3; Wang, Yi4,5
2019-08-15
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume267Issue:5Pages:2737-2791
AbstractWe 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.
DOI10.1016/j.jde.2019.03.030
Language英语
Funding ProjectBasic 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 Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000468614700002
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34749
Collection应用数学研究所
Corresponding AuthorWang, Yi
Affiliation1.Sookmyung Womens Univ, Dept Math, Seoul 04310, South Korea
2.Sookmyung Womens Univ, Res Inst Nat Sci, Seoul 04310, South Korea
3.Univ Texas Austin, Dept Math, Austin, TX 78712 USA
4.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China
5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
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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