Existence and asymptotic behavior of global smooth solution for p-System with damping and boundary effect

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	Existence and asymptotic behavior of global smooth solution for p-System with damping and boundary effect
	Zhang, Yinghui ; Tan, Zhong ; Tan Z(谭忠)
刊名	http://dx.doi.org/10.1016/j.na.2009.10.046
	2010-03-01
关键词	NONLINEAR DIFFUSION WAVES PARTIAL-DIFFERENTIAL-EQUATIONS THROUGH POROUS-MEDIA HYPERBOLIC CONSERVATION-LAWS COMPRESSIBLE EULER EQUATIONS CONVERGENCE-RATES SINGULARITIES FLOW RELAXATION SYMMETRY
英文摘要	National Natural Science Foundation of China-NSAF [10976026]; In this paper, we study the existence and asymptotic behavior of global smooth solution for p-System with damping on the strip [0, 1] x (0, infinity) v(t) - u(x) = 0, u(t) + p(v)(x) = -alpha u, with the null-Dirichiet boundary condition, u(0, t) = u(1, t) = 0. First, we prove the existence of the global smooth solution under the assumption that only the C(0)-norm of the first derivatives of the initial data is sufficiently small, while the C(0)-norm of the initial data is not necessarily small. Second, when the initial data is in C(2) and the C(0)-norm of the first derivatives of the initial data is large enough, then the first derivatives of the corresponding C(2) smooth solution must blow up in finite time. Finally, we consider the asymptotic behavior of the global smooth solution. Precisely, we show that the solution of this problem tends to the corresponding nonlinear diffusive wave governed by the classical Darcy's law exponentially fast as time goes to infinity in the sense of H(1)-norm, provided the initial total mass is the same and thus justifies the validity of Darcy's law in large time. (C) 2009 Elsevier Ltd. All rights reserved.
语种	英语
出版者	NONLINEAR ANAL-THEOR
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91042]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Zhang, Yinghui,Tan, Zhong,Tan Z. Existence and asymptotic behavior of global smooth solution for p-System with damping and boundary effect[J]. http://dx.doi.org/10.1016/j.na.2009.10.046,2010.
APA	Zhang, Yinghui,Tan, Zhong,&谭忠.(2010).Existence and asymptotic behavior of global smooth solution for p-System with damping and boundary effect.http://dx.doi.org/10.1016/j.na.2009.10.046.
MLA	Zhang, Yinghui,et al."Existence and asymptotic behavior of global smooth solution for p-System with damping and boundary effect".http://dx.doi.org/10.1016/j.na.2009.10.046 (2010).