关键词：
zero dissipation limit;compressible Navier-Stokes equations;shock waves;initial layers
摘要：
We investigate the zero dissipation limit problem of the one dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that the unique solution to the Navier-Stokes equations exists for all time, and converges to the Riemann solution to the corresponding Euler equations with the same Riemann initial data uniformly on the set away from the shocks, as the viscosity vanishes. In contrast to previous related works, where either the composite wave is absent or the effects of initial layers are ignored, this gives the first mathematical justification of this limit for the compressible isentropic Navier-Stokes equations in the presence of both composite wave and initial layers. Our method of proof consists of a scaling argument, the construction of the approximate solution and delicate energy estimates.
作者机构：
华中师范大学数学与统计学学院 武汉430079;湖北科技学院数学与统计学院 咸宁437100;[陈生安] School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China, School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China
通讯机构：
[Chen, S.] S;School of Mathematics and Statistics, Central China Normal University, China
期刊：
Journal of Biological Systems,2013年21(4):1340003 ISSN：0218-3390
通讯作者：
Yang, Cuihong
作者机构：
[Yang, Cuihong] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Li, Jia] Univ Alabama, Dept Math Sci, Huntsville, AL 35899 USA.
通讯机构：
[Yang, Cuihong] C;Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
关键词：
Transgenes;Mosquitoes;Transformations
摘要：
We formulate a continuous-time 3D model system for the interactive mosquito populations with two different transgenes. We assume that the transgenes are dominant over the wild gene and that one of the transgenes is dominant over the other transgene. Using transformations, we translate the model system to its topologically equivalent 2D system. Based on the investigations of the reduced two-dimensional system, we obtain conditions for the existence and stability of boundary and positive equilibria. We provide numerical examples to demonstrate the rich and complex dynamical features of the model system.
摘要：
Of concern are two classes of convoluted C-regularized operator families: convoluted C-cosine operator families and convoluted C-semigroups. We obtain new and general multiplicative and additive perturbation theorems for these convoluted C-regularized operator families. Two examples are given to illustrate our abstract results.
期刊：
International Journal of Computer Mathematics,2013年90(2):246-257 ISSN：0020-7160
通讯作者：
Peng, J.(pengjin01@tsinghua.org.cn)
作者机构：
[Zhang, Bo] School of Mathematics and Statistics, Huazhong Normal University, Hubei, 430079, China;[Peng, Jin] Institute of Uncertain Systems, Huanggang Normal University, Hubei, 438000, China
通讯机构：
[Jin Peng] I;Institute of Uncertain Systems, Huanggang Normal University, Hubei, 438000, China
摘要：
In practical applications of graph theory, due to some reasons, different types of uncertainties are frequently encountered. In this paper, we employ uncertainty theory to investigate an uncertain graph in which complete determination of whether two vertices are joined by an edge or not cannot be carried out. By means of uncertainty theory, the concepts of connectedness strength of two vertices in an uncertain graph and strength of an uncertain path are proposed. A method to calculate the connectedness strength of two vertices is also described. After that, we investigate the relationship between the connectedness strength of two vertices and the connectedness index of the uncertain graph. This relationship provides a new method to obtain the connectedness index of an uncertain graph.
作者机构：
[Li, Gongbao; Ye, Hongyu] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Gongbao] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
existence;positive solutions;elliptic system;linking geometric structure;zero mass case
摘要：
In this paper, we prove the existence of at least one positive solution pair (u, v) is an element of D-1,D-2 (R-N) x D-1,D-2 (R-N) to the following semilinear elliptic system [GRAPHICS] by using a linking theorem, where K(x) is a positive function in L-s(R-N) for some s > 1 and the nonnegative functions f, g is an element of C(R,R) are of quasicritical growth, superlinear at infinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problem -Delta u = K (x) f (u), x is an element of R-N, and a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R-N.
