THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

1IntroductionThispaperisconcernedwithpositivesolutionOfthesemilinearheatequationswithlocalizedreactionssubjecttoeitherinitialconditions(Cauchyproblem)ortheinitialandboundary-value(DirichletorNeumanntype)conditionswherenisaboundeddomaininRe,icEO.Equations(1.1)canbethoughtofasamodeltodescribesomephysicalphenomena(heatpropagation,chemicalreaction)inwhichthenonlinearreactionsinadynndcalsystemtakesplaceonlyatasinglesite.InthesequelforconvenienceweshallsamplycalltheCauchy,initial-Direchlet,orini…     

THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

1IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblem,where"o(x)isnon-negativesmoothfunctionsatisfying"o.(0)=0,"o.(1)=1'Whenconsideringtheblow-upofsolution,thefollowingproblemarisenaturally:Doesblow-upoccur?Howdoesthesolutionapproachtheblow-uptime'!Andwilersisthehotspotlocated(blow-upset)?WelookattheheatequationwithanonlillearboundaryconditiollHerefiisaboundeddomaininR",p>1isarealnumber.IthasbeenknownforalongtimethattheDroblelil(1.1).(1.2)withAL(~,0)--'no(x)doesnothaveaglobals…     

一类浮游生物植化相克抛物方程

研究2种群竞争抑制系统，利用上下解的方法给出了抛物方程组解的存在性和惟一性的证明，讨论对应常微分方程组平衡解的全局稳定性。给出相应椭圆系统的Harnack不等式．并通过构造Lyapunov泛函说明在种群内部竞争激烈或扩散系数足够大的条件下，其对应的椭圆系统没有非常数解．     

一类SEI传染病扩散模型及其移动边沿

该文研究一类SEI传染病模型,其中病毒在潜伏期和感染期具有感染性.首先研究固定区域上SEI偏微分方程组,考虑平衡解的局部稳定性和全局稳定性.然后重点研究相应的自由边界问题,其中自由边界表示病毒的移动边沿。给出了该问题解的全局存在性、唯一性,讨论了自由边界的性质,证明了病毒要么蔓延,要么消退.还给出了蔓延和消退的充分条件,结果表明:当有效接触率很小或平均潜伏期较短,且初始染病区域小时,疾病消退;而当有效接触率大或平均潜伏期较长,且初始染病区域大时,疾病蔓延.     

扬州城新冠疫情清零防控模式的建模和分析

新冠德尔塔病毒通过境外输入在广州、南京、扬州等地区局部散发.在中国政府强有力的监管防控政策和全市人民的密切配合下,通过“追踪-检测-隔离”清零防控模式,找出“零号病人”,确定传染链,进行全员核酸检测精准筛查密切接触者,并及时采取不同等级的隔离措施,阻断传染链,多地小规模的聚集性疫情在近一个月内能够得以控制.本文以扬州市COVID-19疫情防控为研究对象,通过区分社区和集中隔离点的感染者,建立了具有隔离和大规模检测的传染病模型,研究当前清零模式成功的机制,并利用相关参数模拟了扬州的抗疫成功的过程.利用新模型,我们比较分析“躺平”模式,消极模式以及推迟当前清零政策等,研究了多种情形下的疫情发展趋势及其影响.     

Analysis to Some Solutions Obtained by Modified Extended tanh-Function Method＊

First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplified modified extended tanh-function method. Then, further analysis to some tanh-coth type solutions of nonlinear evolution equations are given. The results show that when balance number m is one or two, the tanh-eoth type solutions obtained by the modified extended tanh-funetion method can be obtained by using the hyperbolic-function method.     

POSITIVE SOLUTIONS TO SYSTEMS OF HEAT EQUATIONS WITH A SEMILINEAR BOUNDARY CONDITION

ＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＴＯＳＹＳＴＥＭＳＯＦＨＥＡＴＥＱＵＡＴＩＯＮＳＷＩＴＨＡＳＥＭＩＬＩＮＥＡＲＢＯＵＮＤＡＲＹＣＯＮＤＩＴＩＯＮＬＩＮＺＨＩＧＵＩ（林支桂）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｖｅｒ...     

增长区域上一类寄生虫-宿主模型的Turing不稳定

为理解区域演化对寄生虫-宿主Turing不稳定的影响,本文以寄生虫-宿主传染病模型为主体,研究增长区域上的反应扩散问题,通过线性化和谱分析给出模型产生Turing不稳定的条件,再利用数值模拟验证理论结果.结果表明扩散系数的增加有利于Turing斑图的形成,而区域增长对Turing斑图形成起破坏作用.