Einstein-de Sitter时空上具有非线性记忆项的半线性阻尼波动方程解的爆破  

Blow-up of Solutions to a Semilinear Damped Wave Equation with a Nonlinear Memory Term in Einstein-de Sitter Spacetime

作　　者：欧阳柏平 OUYANG Baiping(School of Data Science,Guangzhou Huashang College,Guangzhou 511300,China)

机构地区：[1]广州华商学院数据科学学院,广东广州511300

出　　处：《应用数学》2022年第4期909-917,共9页Mathematica Applicata

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);广州市哲学社会科学发展”十三五”规划课题(2019GZGJ209)。

摘　　要：本文考虑Einstein-de Sitter时空上一类非线性记忆项的半线性阻尼波动方程解的爆破现象.通过应用修正贝塞尔方程和迭代技巧,推出了其柯西问题在次临界情况下解的全局非存在性.同时,还得到了解的生命跨度上界估计.Blow-up of solutions to a semilinear damped wave equation with a nonlinear memory term in Einstein-de Sitter spacetime is considered.By applying a modified Bessel equation and an iteration technique,the nonexistence of solutions to the Cauchy problem for the semilinear damped wave equation in the subcritical case is derived.Also,an upper bound estimate of solutions for the lifespan is obtained.

关 键 词：非线性记忆项 波动方程 Einstein-deSitter时空 爆破 

分 类 号：O175.2[理学—数学]