Stability of planar diffusion wave for nonlinear evolution equation

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	Stability of planar diffusion wave for nonlinear evolution equation
其他题名	Stability of planar diffusion wave for nonlinear evolution equation
	He Cheng 1; Huang FeiMin2 ; Yong Yan 3
	2012-01-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	55 期号:2 页码:337-352
摘要	It is known that the one-dimensional nonlinear heat equation u(t) = f(u)(x1 x1), f' (u) > 0, u(+/-infinity, t) = u(+/-), u(+) not equal u(-) has a unique self-similar solution (u) over bar( x(1)/root 1+t). In multi-dimensional space, (u) over bar( x(1)/root 1+t) is called a planar diffusion wave. In the first part of the present paper, it is shown that under some smallness conditions, such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation: u(t) - Delta f(u) = 0, x is an element of R-n. The optimal time decay rate is obtained. In the second part of this paper, it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with clamping: u(tt) + u(t) - Delta f(u) = 0, x is an element of R-n. The time decay rate is also obtained. The proofs are given by an elementary energy method.
其他摘要	It is known that the one-dimensional nonlinear heat equation u_t = f(u)_(x_1x_1),f’(u) > 0,u(±∞,t) = u±,u+ ≠ u_ has a unique self-similar solution u(x_1/1+t~(1/2)).In multi-dimensional space,u(x_1/1+t~(1/2)) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:u_t-△f(u) = 0,x ∈ R~n.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping: u_(tt) + u_t - △f(u) = 0,x ∈ R~n.The time decay rate is also obtained.The proofs are given by an elementary energy method.
关键词	HYPERBOLIC CONSERVATION-LAWS THROUGH POROUS-MEDIA P-SYSTEM ASYMPTOTIC-BEHAVIOR CONVERGENCE FLOW MULTIDIMENSIONS RATES stability planar diffusion wave nonlinear evolution equation
收录类别	CSCD
语种	英语
资助项目	[National Basic Research Program of China] ; [National Natural Science Foundation of China for Distinguished Youth Scholar] ; [NSFC-NSAF]
CSCD记录号	CSCD:4537845
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/56366
专题	应用数学研究所
作者单位	1.Natl Nat Science Fdn China, Beijing I00085, Peoples R China 2.中国科学院数学与系统科学研究院 3.上海大学
推荐引用方式 GB/T 7714	He Cheng,Huang FeiMin,Yong Yan. Stability of planar diffusion wave for nonlinear evolution equation[J]. SCIENCE CHINA-MATHEMATICS,2012,55(2):337-352.
APA	He Cheng,Huang FeiMin,&Yong Yan.(2012).Stability of planar diffusion wave for nonlinear evolution equation.SCIENCE CHINA-MATHEMATICS,55(2),337-352.
MLA	He Cheng,et al."Stability of planar diffusion wave for nonlinear evolution equation".SCIENCE CHINA-MATHEMATICS 55.2(2012):337-352.