非线性记忆项的Euler-Poisson-Darboux-Tricomi方程解的爆破  

Blow-up of Solutions to the Euler-Poisson-Darboux-Tricomi Equation with a Nonlinear Memory Term

作　　者：欧阳柏平 Baiping Ouyang(Department of Apllied Mathematics,Guangzhou Huashang College,Guangzhou 511300)

机构地区：[1]广州华商学院应用数学系,广州511300

出　　处：《数学物理学报（A辑）》2023年第1期169-180,共12页Acta Mathematica Scientia

基　　金：广东省普通高校自然科学重点项目(2019KZDXM042);广东省普通高校创新团队项目(2020WCXTD008);广州华商学院校内项目(2020HSDS01,2021HSKT01)。

摘　　要：研究了具有非线性记忆项的Euler-Poisson-D arboux-Tricomi方程在次临界情况下解的爆破现象.利用泛函分析方法结合修正的Bessel方程推出了其柯西问题解的迭代框架和第一下界,然后通过迭代技巧,获得了其解的全局非存在性以及解的生命跨度上界估计.Blow-up phenomenon of solutions to the Euler-Poisson-Darboux-Tricomi equation with a nonlinear memory term in the subcritical case is studied.By using functional methods associated with a modified Bessel equation,an iteration frame and the first lower bound are derived.Then,nonexistence of global solutions to the Cauchy problem for the EulerPoisson-Darboux-Tricomi equation and an upper bound estimate of solutions for the lifespan are obtained via the iteration technique.

关 键 词：非线性记忆项 Euler-Poisson-Darboux-Tricomi方程 爆破 

分 类 号：O175.2[理学—数学]