On a nonhomogeneous Burgers' equation

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	On a nonhomogeneous Burgers' equation
	Ding, XQ; Jiu, QS ; He, C
	2001-08-01
发表期刊	SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY
ISSN	1006-9283
卷号	44 期号:8 页码:984-993
摘要	In this paper the Cauchy problem for the following nonhomogeneous Burgers' equation is considered: (1) u(t) + uu(x) = muu(xx) - kx, x is an element of R, t > 0, where mu and k are positive constants. Since the nonhomogeneous term kx does not belong to any LP( R) space, this type of equation is beyond usual Sobolev framework in some sense. By Hopf-Cole transformation, (1) takes the form (2) phi(t) = phi(xx) = -x(2)phi. With the help of the Hermite polynomials and their properties, (1) and (2) are solved exactly. Moreover, the large time behavior of the solutions is also considered, similar to the discussion in Hopf's paper. Especially, we observe that the nonhomogeneous Burgers' equation (1) is nonlinearly unstable.
关键词	nonhomogeneous Burgers' equation explicit solution large time behavior Hermite polynomials
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000174374300005
出版者	SCIENCE CHINA PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/16903
专题	应用数学研究所
通讯作者	Jiu, QS
作者单位	1.Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Ding, XQ,Jiu, QS,He, C. On a nonhomogeneous Burgers' equation[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,2001,44(8):984-993.
APA	Ding, XQ,Jiu, QS,&He, C.(2001).On a nonhomogeneous Burgers' equation.SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,44(8),984-993.
MLA	Ding, XQ,et al."On a nonhomogeneous Burgers' equation".SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY 44.8(2001):984-993.