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.
作者机构：
[Li, Jun-Feng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Liu, Wei-An] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.
通讯机构：
[Li, Jun-Feng] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
In this paper, we study a chemotaxis system involving two interacting species as follows: partial derivative u/partial derivative t = D(u)del.(u del(ln(u/Phi(x, t, w))) + f(x,t,u,v), partial derivative v/partial derivative t = D(v)Delta v + g(x, t, u, v), partial derivative w/partial derivative t = h(x, t, u, w), with some initial and boundary conditions. We prove the existence of solution to the problem whose behavior is concerned with reference to some systems through sup-sub-solution method.
作者机构：
[Yao, Xiangjuan] China Univ Min & Technol, Coll Sci, Xuzhou 221116, Jiangsu, Peoples R China.;[Li, Xiangwen] Huazhong Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.;[Lai, Hong-Jian] W Virginia Univ, Dept Math, Morgantown, WV 26506 USA.
通讯机构：
[Yao, Xiangjuan] C;China Univ Min & Technol, Coll Sci, Xuzhou 221116, Jiangsu, Peoples R China.
作者机构：
[Feng, Yanqin; Hu, Xia] School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;[Li, Shuchao] Faculty of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Science, Central China Normal University, Wuhan 430079, China
通讯机构：
[Li, S.] F;Faculty of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Science, Central China Normal University, Wuhan 430079, China
摘要：
In this paper, we have investigated the existence and the multiplicity of the equatorial limit cycle for a class of planar vector fields of degree 2m+1, obtained the necessary and sufficient condition that the equator is a closed orbit and the multiplicity of the equatorial limit cycle of the planar polynomial vector fields is m+1. It is helpful to answer the second part of Hilbert’s 16th problem.
作者机构：
[Cheng, Luan] Huazhong Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Enke; Cheng, Luan] Huazhong Normal Univ, Inst Particle Phys, Wuhan 430079, Peoples R China.
通讯机构：
[Cheng, Luan] H;Huazhong Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.
会议名称：
10th International Conference on Nucleus-Nucleus Collisions (NN2009)
会议时间：
AUG 16-21, 2009
会议地点：
Beijing, PEOPLES R CHINA
会议主办单位：
[Cheng, Luan] Huazhong Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.^[Cheng, Luan;Wang, Enke] Huazhong Normal Univ, Inst Particle Phys, Wuhan 430079, Peoples R China.
摘要：
We report the evolution effects on jet energy loss with detailed balance. The initial conditions and parton evolution based on perturbative QCD in the chemical non-equilibrated medium and Bjorken expanding medium at RHIC are determined. The parton evolution affect the jet energy loss evidently. This will increase the energy and propagating distance dependence of the parton energy loss and will affect the shape of suppression of moderately high P_{T} hadron spectra. Comment: 4 pages, 2 figures, procedding of NN2009
作者机构：
[Huan Qi] Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China;School of Mathematics and Statistics, Huazhong Normal University, Wuhan, Hubei, China;[Qiong Fan] Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China<&wdkj&>School of Mathematics and Statistics, Huazhong Normal University, Wuhan, Hubei, China
通讯机构：
[Huan Qi] D;Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China
关键词：
2-walk linear graphs;unicyclic graphs;bicyclic graphs;tricyclic graphs
作者机构：
[Zhang, Xinan; Ma, Lianhua; Yang, Cuihong] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
会议名称：
7th Conference on Biological Dynamic System and Stability of Differential Equation
会议时间：
MAY 14-16, 2010
会议地点：
Chongqing, PEOPLES R CHINA
会议主办单位：
[Yang, Cuihong;Ma, Lianhua;Zhang, Xinan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Limit cycle;invariant cone;vector field
摘要：
In this paper, we have found a bridge between a class of cubic vector fields in R-3 and the tangent vector fields of two-dimensional manifold S-2, and have proved the existence of at least 5 isolated closed orbits for a class of cubic system in R-3, which are located on the five invariant closed cones of the system.
