带有反馈与起动故障的M/G/1重新访问排队系统的适定性分析

文章研究一个带有贝努利反馈且系统服务台经常遭受启动故障的重新访问排队系统模型,利用线性算子半群理论,通过对描述其系统行为的偏微分方程组的研究,证明了该模型所描述的系统所确定的算子是闭稠定耗散算子,生成C0压缩半群,从而得到系统的适定性.在证明1是算子的预解点时,采用了共轭方法.     

Equivalence of three kinds of well-posed-ness of discontinuous Riemann-Hilbert problem for elliptic complex equation in multiply connected domains

In this article, we first introduce the general linear elliptic complex equation of first order with certain conditions, and then propose discontinuous Riemann-Hilbert problem and some kinds of modified well-posed-ness for the complex equation. Then we verify the equivalence of three kinds of well-posed-ness. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.     

带有发病年龄的HIV/AIDS传播的数学建模及分析

所建的模型是用含有常微分方程和偏微分方程的方程组来描述的,考虑了垂直感染,发病年龄,AIDS病人有希望恢复到潜伏期以及不同患者接受治疗的能力不同等诸多因素.利用导出的方程,直接推出:当AIDS引起死亡率增加时,社会总人口衰减.利用泛函分析方法和有界线性算子半群理论分析了系统的适定性,并证明了系统方程存在正解.