This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of R^N. Based on the Galerkin method, Brouwer's theorem and the weighted compact Sobolev-type embedding theorem, a new result about the existence of solutions is revealed to the problem.
In this paper, the global well-posedness of the three-dimensional incompressible Navier-Stokes equations with a linear damping for a class of large initial data slowly varying in two directions are proved by means of a simpler approach.
针对WSN动态覆盖问题可以转化为多目标优化问题,提出一种解决动态覆盖问题的启发式算法UGA(Uniform Genetic Algorithm)。该算法定义出多目标优化问题,为了保证最优解的多样性,提出一种解均匀策略(Solution Even Tactics,SET)进行Pareto最优解适应度更新。实验结果表明,在不同网络规模和迭代次数下,区域覆盖度和网络寿命相对于传统经典算法有较好改进。
This paper aims at analyzing the shapes of the bounded traveling wave solutions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and conditions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefcients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approximate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate solutions. It can be seen that the error is infinitesimal decreasing in the exponential form.
In this paper, we study the orbital stability of solitary waves of compound KdV-type equation in the form of ut + aupux + bu2 pux + uxxx = 0(b≥0, p > 0). Our results imply that orbital stability of solitary waves is affected not only by the highest-order nonlinear term bu2 pupx, but also the nonlinear term auux. For the case of b > 0 and 0 < p≤2, we obtain that the positive solitary wave u1(x-ct) is stable when a > 0, while that unstable when a < 0. The stability for negative solitary wave u2(x-ct) is on the contrary. In particular,we point that the nonlinear term with coefficient a makes contributes to the stability of the solitary waves when p = 2 and a > 0.
This paper deals with a bi-extrapolated subgradient projection algorithm by introducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved under some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.
利用软件即服务(SaaS)模式中软件服务和多用户租赁的特点,提出一种动态信息门户开发框架(dynamic information portal framework for SaaS model,DIPFS),替代传统ASP模式开发动态网站,以满足现代大数据规模上的增量需求。DIPFS的数据存储服务采用SaaS第四级成熟度设计,支持面向集群水平方向的自由扩展;从领域工程的角度出发,用eJackson图描述网页构件的特征模型,完成DIPFS核心的页面生成功能;以一个动态图片部件的实现过程为例,描述DIPFS提供的共用软件服务并展示生成页面的最终效果。
