摘要：
In this paper, we study the one-dimensional Navier-Stokes equations connecting to vacuum state with a jump in density when the viscosity depends on the density. Precisely, when the viscosity coefficient μ(ρ) is proportional to ρ
θ
with θ > 0, where ρ is the density, we give the asymptotic behavior and the decay rate of the density function ρ(x, t). Furthermore, the behavior of the density function ρ(x, t) near the interfaces separating the gas from vacuum and the expanding rate of the interfaces are also studied. The analysis is based on some new mathematical techniques and some new useful estimates. This fills a final gap on studying Navier-Stokes equations with the viscosity coefficient μ(ρ) dependent on the density ρ.
期刊：
Linear Algebra and its Applications,2009年430(1):370-385 ISSN：0024-3795
通讯作者：
Li, Xuechao
作者机构：
[Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Li, Xuechao] Univ Georgia, Div Acad Enhancement, Athens, GA 30602 USA.
通讯机构：
[Li, Xuechao] U;Univ Georgia, Div Acad Enhancement, Athens, GA 30602 USA.
关键词：
Graphs;Energy;Eigenvalue
摘要：
The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Let G(n,d) be the class of tricyclic graphs G on n vertices with diameter d and containing no vertex disjoint odd cycles Cp,Cq of lengths p and q with p+q≡2(mod4). In this paper, we characterize the graphs with minimal energy in G(n,d).
作者机构：
[陈刚] School of Math.and Statistics,Central China Normal University;[王荣乾] Henan Polytechnic Institute;[孙大英] School of Information,Renmin University of China
期刊：
Linear Algebra and its Applications,2009年431(10):1848-1857 ISSN：0024-3795
通讯作者：
Li, Shuchao
作者机构：
[Hu, Zhiquan; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Zhu, Chunfeng] Guangdong Sun Yat Sen Mem Middle Sch, Zhongshan 528454, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Spectra of a graph;Main eigenvalues;Bicyclic graphs;2-Walk linear graphs
期刊：
Communications in Partial Differential Equations,2009年34(12):1566-1591 ISSN：0360-5302
通讯作者：
Peng, Shuangjie
作者机构：
[Daomin Cao] Chinese Acad Sci, Inst Appl Math, AMSS, Beijing, Peoples R China.;[Shuangjie Peng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Peng, Shuangjie] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Bound states;Concentrating solutions;Critical point;Potential vanishing or unbounded at infinity;Variational method
摘要：
In this paper we study the existence and qualitative property of standing wave solutions for the nonlinear Schrödinger equation . Let . For any integer k ≥ 1, we prove existence of standing wave solutions with u > 0 having k local maximum points and concentrating near a given local maximum point of Γ when ε is small. The potentials V and K are allowed to be either vanishing or unbounded at infinity. Existence of solutions concentrating near k distinct non-degenerate critical points of Γ has been proved under the same assumptions on V and K as well.
期刊：
Journal of Mathematical Analysis and Applications,2009年356(2):711-728 ISSN：0022-247X
通讯作者：
Yao, Xiaohua
作者机构：
[Ding, Yong] Beijing Normal Univ, Minist Educ, Lab Math & Complex Syst, Sch Math Sci, Beijing 100875, Peoples R China.;[Yao, Xiaohua] Huazhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Yao, Xiaohua] H;Huazhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
关键词：
Dispersive equation;L-p-L-q estimate;Oscillatory integral;Integrated group
摘要：
This paper is mainly concerned with the L-p-L-q estimates of solutions for a class of general dispersive equations under the condition (H-b) with an index b is an element of (0, 1). To the end. the new pointwise decay estimates of oscillatory integrals related to the fundamental solutions are proved. If b = 1, then the pointwise estimates are particularly consistent with the sharp results of the nondegenerate cases. Moreover, as an application of the L-p-L-q estimates, we also show that higher-order differential operator iP(D) + V(x, D) generates a fractionally integrated group on some L-p(R-n), from which certain L-p-estimates for the solutions of generalized Schrodinger equations are obtained. (c) 2009 Elsevier Inc. All rights reserved.
摘要：
In the present paper a class of extended close-to-convex functions Q_k,λ (α,β,ρ) defined by making use of Ruscheweyh derivatives is introduced and studied. We provide integral rep-resentations, distortion theorem, radius of close-to-convexity and Hadamard product properties for this class.
