L-1-CONVERGENCE TO GENERALIZED BARENBLATT SOLUTION FOR COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDENT DAMPING

doi:10.1137/20M1361043

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	L-1-CONVERGENCE TO GENERALIZED BARENBLATT SOLUTION FOR COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDENT DAMPING
	Geng, Shifeng 1; Huang, Feimin2,3 ; Wu, Xiaochun2
	2021
Source Publication	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN	0036-1410
Volume	53 Issue:5 Pages:6048-6072
Abstract	In this paper, the large time behavior of an entropy solution to the compressible Euler equations for polytropic gas (the pressure p(rho) = kappa rho(gamma), gamma > 1) with time-dependent damping like -1/(1+t)(lambda)rho u (0 < lambda < 1) is investigated. By introducing an elaborate iterative method and using intensive entropy analysis, it is proved that the L-infinity entropy solution of compressible Euler equations with finite initial mass converges strongly in the natural L-1 topology to a fundamental solution of the porous medium equation (PME) with time-dependent diffusion, called a generalized Barenblatt solution. It is interesting that the L-1 decay rate is getting faster and faster as lambda increases in (0, gamma/gamma+2], while is getting slower and slower in [gamma\gamma+2, 1).
Keyword	convergence rates compressible Euler equations generalized Barenblatt solution time-dependent damping compensated compactness
DOI	10.1137/20M1361043
Indexed By	SCI
Language	英语
Funding Project	National Natural Science Foundation of China[12071397] ; National Natural Science Foundation of China[11688101] ; Excellent Youth Project of Hunan Education Department[18B054]
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied
WOS ID	WOS:000749346300033
Publisher	SIAM PUBLICATIONS
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/59969
Collection	应用数学研究所博士后
Corresponding Author	Wu, Xiaochun
Affiliation	1.Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation GB/T 7714	Geng, Shifeng,Huang, Feimin,Wu, Xiaochun. L-1-CONVERGENCE TO GENERALIZED BARENBLATT SOLUTION FOR COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDENT DAMPING[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2021,53(5):6048-6072.
APA	Geng, Shifeng,Huang, Feimin,&Wu, Xiaochun.(2021).L-1-CONVERGENCE TO GENERALIZED BARENBLATT SOLUTION FOR COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDENT DAMPING.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,53(5),6048-6072.
MLA	Geng, Shifeng,et al."L-1-CONVERGENCE TO GENERALIZED BARENBLATT SOLUTION FOR COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDENT DAMPING".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 53.5(2021):6048-6072.

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