一类带全局反应项SIR传染病模型的异宿轨和行波解（英文）

本文研究一类SIR类型传染病模型的正异宿轨的存在性问题,该类模型通常被视为带全局反应项和非单调型的时滞微分方程组.利用Fraia和黄等发展的Freedholm算子分解及非线性扰动理论,我们研究反应扩散系统的行波解和对应时滞微分方程异宿轨解之间的关联性,并据此证明该系统行波解的存在性和动力学性质.     

求解分数阶延迟微分方程的卷积Runge-Kutta方法

本文利用强A-稳定Runge-Kutta方法求解一类非线性分数阶延迟微分方程初值问题,并给出了算法的稳定性和误差分析.数值算例验证算法的有效性及其相关理论结果.     

沿任意直线方向逃逸的鱼雷击舰问题

研究了战舰沿任意直线方向逃逸时的鱼雷击舰问题,通过坐标旋转变换求解了鱼雷的运动轨迹方程的解析解.     

具有次线性中立项的二阶半线性微分方程的振动准则

研究一类具有次线性中立项的半线性微分方程的振动性.建立了新的振动准则,推广和改进了文献中若干新结果.     

一类具有p-Laplacian算子的非线性分数阶微分方程m点边值问题解的存在性

讨论具有p-Laplacian算子的非线性分数阶微分方程m点边值问题的解的存在性,研究结果是建立在不动点定理和压缩映射原理基础上.此外给出两个例子来说明结果.     

Extinction Effects of Multiplicative Non-Gaussian L′evy Noise in a Tumor Growth System with Immunization

The extinction phenomenon induced by multiplicative non-Gaussian Levy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in terms of a stochastic differential equation with multiplicative noise. By means of the theory of the infinitesimal generator of Hunt processes, the escape probability, which is used to measure the noise-induced extinction probability of tumor cells, is explicitly expressed as a function of initial tumor cell density, stability index and noise intensity. Based on the numerical calculations, it is found that for different initial densities of tumor cells, noise parameters play opposite roles on the escape probability. The optimally selected values of the multiplicative noise intensity and the stability index are found to maximize the escape probability.     

Preface

This special issue is originated from the workshop on ＂Recent Developments in Numerical Methods for Nonlinear Hyperbolic Partial Differential Equations and their Applications＂ held on September 1-5, 2008, at Banff International Research Station for Mathematical Innovation and Discovery, in Banff, Alberta, Canada. The workshop was organized by Ian Mitchell （University of British Columbia）, Stanley Osher （University of California, Los Angeles）, Chi-Wang Shu （Brown University） and Hongkai Zhao （University of California, Irvine）.