L-2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws

doi:10.1016/j.jde.2019.03.030

CSpace > 应用数学研究所

	L-2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws
	Kang, Moon-Jin 1,2; Vasseur, Alexis F.3; Wang, Yi4,5
	2019-08-15
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	267 期号:5 页码:2737-2791
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.
DOI	10.1016/j.jde.2019.03.030
语种	英语
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
WOS类目	Mathematics
WOS记录号	WOS:000468614700002
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34749
专题	应用数学研究所
通讯作者	Wang, Yi
作者单位	1.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
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.