Convergence to the barenblatt solution for the compressible euler equations with damping and vacuum

doi:10.1007/s00205-004-0349-y

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	Convergence to the barenblatt solution for the compressible euler equations with damping and vacuum
	Huang, FM; Marcati, P ; Pan, RH
	2005-03-01
发表期刊	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN	0003-9527
卷号	176 期号:1 页码:1-24
摘要	We study the asymptotic behavior of a 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 -> infinity, 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 give a definite answer to this conjecture without any assumption on smallness or regularity for the initial data. We prove that any L-infinity weak entropy solution to the Cauchy problem of damped Euler equations with finite initial mass converges, strongly in L-p with decay rates, to matching Barenblatt's profile of the porous medium equation. The density function tends to the Barenblatt's solution of the porous medium equation while the momentum is described by Darcy's law.
DOI	10.1007/s00205-004-0349-y
语种	英语
WOS研究方向	Mathematics ; Mechanics
WOS类目	Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000228225600001
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/1304
专题	应用数学研究所
通讯作者	Huang, FM
作者单位	1.Acad Sinica, Inst Appl Math, AMSS, Beijing 100080, Peoples R China 2.Univ Aquila, Dipartimento Matemat Pura & Applicata, I-67100 Laquila, Italy 3.Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA
推荐引用方式 GB/T 7714	Huang, FM,Marcati, P,Pan, RH. Convergence to the barenblatt solution for the compressible euler equations with damping and vacuum[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2005,176(1):1-24.
APA	Huang, FM,Marcati, P,&Pan, RH.(2005).Convergence to the barenblatt solution for the compressible euler equations with damping and vacuum.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,176(1),1-24.
MLA	Huang, FM,et al."Convergence to the barenblatt solution for the compressible euler equations with damping and vacuum".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 176.1(2005):1-24.