L (1) Convergence to the Barenblatt Solution for Compressible Euler Equations with Damping

doi:10.1007/s00205-010-0355-1

CSpace > 应用数学研究所

	L (1) Convergence to the Barenblatt Solution for Compressible Euler Equations with Damping
	Huang, Feimin1 ; Pan, Ronghua 2; Wang, Zhen 3
	2011-05-01
发表期刊	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN	0003-9527
卷号	200 期号:2 页码:665-689
摘要	We study the asymptotic behavior of compressible isentropic flow through a porous medium when the initial mass is finite. The model system is the compressible Euler equation with frictional damping. As t -> a, the density is conjectured to obey the well-known porous medium equation and the momentum is expected to be formulated by Darcy's law. In this paper, we prove that any L (a) weak entropy solution to the Cauchy problem of damped Euler equations with finite initial mass converges strongly in the natural L (1) topology with decay rates to the Barenblatt profile of the porous medium equation. The density function tends to the Barenblatt solution of the porous medium equation while the momentum is described by Darcy's law. The results are achieved through a comprehensive entropy analysis, capturing the dissipative character of the problem.
DOI	10.1007/s00205-010-0355-1
语种	英语
资助项目	NSFC[10825102] ; NSFC[10871199] ; NSFC-NSAF[10676037] ; 973 project of China[2006CB805902] ; National Science Foundation[DMS-0807406]
WOS研究方向	Mathematics ; Mechanics
WOS类目	Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000289433500009
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11398
专题	应用数学研究所
通讯作者	Huang, Feimin
作者单位	1.Acad Sinica, Inst Appl Math, AMSS, Beijing 100080, Peoples R China 2.Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA 3.Acad Sinica, Inst Phys & Math, Wuhan, Peoples R China
推荐引用方式 GB/T 7714	Huang, Feimin,Pan, Ronghua,Wang, Zhen. L (1) Convergence to the Barenblatt Solution for Compressible Euler Equations with Damping[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2011,200(2):665-689.
APA	Huang, Feimin,Pan, Ronghua,&Wang, Zhen.(2011).L (1) Convergence to the Barenblatt Solution for Compressible Euler Equations with Damping.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,200(2),665-689.
MLA	Huang, Feimin,et al."L (1) Convergence to the Barenblatt Solution for Compressible Euler Equations with Damping".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 200.2(2011):665-689.