作者机构：
[Hu, Song] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Li] East China Jiaotong Univ, Sch Basic Sci, Nanchang 330013, Peoples R China.
通讯机构：
[Wang, Li] E;East China Jiaotong Univ, Sch Basic Sci, Nanchang 330013, Peoples R China.
摘要：
In this paper, we discuss the following fourth-order semilinear elliptic problem {Delta(2)u + c Delta u = f(x, u), x is an element of Omega, u = Delta u = 0, x is an element of partial derivative Omega, where f(x, t) is asymptotically linear with respect to t at infinity. Omega is a smooth bounded domain in R-N and N > 4. In this case, f (x, t) does not satisfy the following Ambrosetti-Rabinowitz type condition (see Ambrosetti and Rabinowitz (1973) [9]), for short, which is called the (AR) condition, that is, for some theta > 0 and M > 0, 0 < F(x, t) (sic) integral(t)(0)f(x, s)ds <= 1/2 + theta f(x, t)t uniformly a.e. x is an element of Omega and for all vertical bar t vertical bar >= M, which is important in applying the mountain pass theorem. By a variant version of the mountain pass theorem, we obtain the existence of nontrivial solutions to the above problem under suitable assumptions of f(x, t), which generalizes and improves the results in Liu and Wang (2007) [12] and An and Liu (2008) [13]. (C) 2013 Elsevier Ltd. All rights reserved.
摘要：
In this paper, we study the existence of global classical solutions and the vanishing diffusion limit of a 3D conservation laws derived from the well-known Keller-Segel model. First, we establish the global well-posedness of classical solutions to the Cauchy problem for the model with smooth initial data which is of small L (2) norm, together with some a priori estimates uniform for t and . Then, we investigate the zero diffusion limit and get the global well-posedness of classical solutions to the Cauchy problem for the non-diffusive model. Finally, we derive the convergence rate of the model toward the non-diffusive model. It is shown that the convergence rate in L (a) norm is of the order . It should be noted that the initial data are small in L (2)-norm but can be of large oscillations with constant state at far field. As a byproduct, we improve the corresponding result on the well-posedness of the non-diffusive model which requires small oscillations.
关键词：
Euler equations with damping;global existence;asymptotic behavior
摘要：
We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.
摘要：
According to the characteristics of fuel transportation problem, the traditional genetic algorithm model is improved in this paper. The complexity of encoding is simplified by considering the condition of putting the distances of the tanker going halfway back and forth into the objective function. Scanning method is used to generate the initial population improving the quality of chromosomes in the initial population. Adopting the way of "interval crossover, random replacement" ensures the effectiveness and randomness of the crossover. Adding the operation of evolutionary cycle after crossover and mutation operation enhances the local search ability of the algorithm. Finally through MATLAB programming, the traditional genetic algorithm, the scanning genetic algorithm and the evolutionary cycle genetic algorithm and the improved genetic algorithm are compared which further verifies that the improved genetic algorithm is effective.
摘要：
Barrier coverage based on Wireless Sensor Networks (WSNs) has been widely used to prevent intruder trespassing in monitoring systems. Traditionally, enabling perfect barrier coverage is considered the most important goal of barrier coverage studies. Imperfect coverage has been deemed to be a failure. In our research, we attempted to use the redundant sensor nodes in WSNs to prolong the optimal network lifetime of barrier coverage by adding imperfect barrier coverage. Specifically, we devised two schemes, CIBC-1 and CIBC-2, to construct imperfect barrier coverage in order to improve the performance of the existing optimal network lifetime scheduling algorithms for barrier coverage. Our simulation results indicate that our schemes can significantly extend the network lifetime resulting from the state-of-the-art network lifetime scheduling algorithms.
期刊：
Journal of Computational Physics,2014年268:377-398 ISSN：0021-9991
通讯作者：
Zhang, Jing
作者机构：
[Wang, Li-Lian] Nanyang Technol Univ, Sch Math & Phys Sci, Div Math Sci, Singapore 637371, Singapore.;[Zhang, Jing] Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Jing] Beijing Computat Sci Res Ctr, Beijing, Peoples R China.;[Zhang, Zhimin] Wayne State Univ, Detroit, MI 48202 USA.
通讯机构：
[Zhang, Jing] H;Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
The first purpose of this paper is to provide further illustrations, from both theoretical and numerical perspectives, for the nonconvergence of h-refinement in hp-approximation by the prolate spheroidal wave functions (PSWFs), a surprising convergence property that was first discovered by Boyd et al. (2013) [3]. The second purpose is to offer a new basis that leads to prolate-collocation systems with condition numbers independent of (c, N), the intrinsic bandwidth parameter and the number of collocation points. We highlight that the collocation scheme together with a very practical rule for pairing up (c, N) significantly outperforms the Legendre polynomial-based method (and likewise other Jacobi polynomial-based methods) in approximating highly oscillatory bandlimited functions. (C) 2014 Elsevier Inc. All rights reserved.
摘要：
Two classes of 3rd order correlation immune symmetric Boolean functions have been constructed respectively in [1] and [2], in which some interesting phenomena of the algebraic degree have been observed as well. However, a good explanation has not been given. In this paper, we obtain the formulas for the degree of these functions, which can well explain the behavior of their degree.
作者机构：
[Peng, Shuangjie; Deng, Yinbin] Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Jixiu] Hubei Univ Arts & Sci, Sch Math & Comp Sci, Xiangyang 441053, Peoples R China.
通讯机构：
[Deng, Yinbin] H;Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
minimisation, Schrodinger equation, solitons
摘要：
This paper is concerned with constructing nodal radial solutions for generalized quasilinear Schrodinger equations in R-N which arise from plasma physics, fluid mechanics, as well as high-power ultashort laser in matter. For any given integer k >= 0, by using a change of variables and minimization argument, we obtain a sign-changing minimizer with k nodes of a minimization problem. (c) 2014 AIP Publishing LLC.
摘要：
In this paper, we study the following nonlinear problem of Kirchhoff type with critical Sobolev exponent: {-(a + b integral(R3) vertical bar Du vertical bar(2)) Delta u + u = f(x, u) + u(5), x is an element of R-3, u is an element of H-1 (R-3), u > 0, x is an element of R-3, where a, b > 0 are constants. Under certain assumptions on the sign-changing function f(x,u), we prove the existence of positive solutions by variational methods. Our main results can be viewed as a partial extension of a recent result of He and Zou in [Journal of Differential Equations, 2012] concerning the existence of positive solutions to the nonlinear Kirchhoff problem {-(epsilon(2)a + epsilon b integral R-3 vertical bar Du vertical bar(2)) Delta u + V(x)u = f(u), x is an element of R-3, u is an element of H-1 (R-3), u > 0, x is an element of R-3, where epsilon > 0 is a parameter, V(x) is a positive continuous potential, and f(u) similar to vertical bar u vertical bar(p-2)u with 4 < p < 6 and satisfies the Ambrosetti-Rabinowitz type condition. Copyright (C) 2013 John Wiley & Sons, Ltd.
摘要：
This paper is a continuation of [13], where we studied the existence and other analytic properties of positive radial solutions for a system of nonlinear Maxwell equations in the plane R-2, which arises in the modelling of mesoscopic scale electromagnetic phenomena. In this paper we derive local estimates of singular positive solutions, based on which a classification theorem of general positive solutions is established. The refined singularity of general positive solutions is also investigated by employing the theory of infinite dimensional dynamical systems. (C) 2013 Elsevier Inc. All rights reserved.
摘要：
We consider a system of nonlinear Maxwell-type equations in the plane, which arises in the modeling of mesoscopic scale electromagnetic phenomena. After reduction to a quasi-linear equation and symmetrization, we obtain an explicit local description of the solutions in the form of power series. Subsequently, we apply general methods to show global existence of the solutions and to analyze their oscillations and asymptotic behavior.
作者机构：
[Li, Jun-feng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Liu, Wei-an; Chen, Hua] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.
通讯机构：
[Chen, Hua] W;Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.
期刊：
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,2014年66(4):844-873 ISSN：0008-414X
通讯作者：
Kuo, Wentang
作者机构：
[Kuo, Wentang; Liu, Yu-Ru] Univ Waterloo, Fac Math, Dept Pure Math, Waterloo, ON N2L 3G1, Canada.;[Zhao, Xiaomei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Kuo, Wentang] U;Univ Waterloo, Fac Math, Dept Pure Math, Waterloo, ON N2L 3G1, Canada.
关键词：
Vinogradov's mean value theorem;function fields;circle method
