具有非线性记忆项的半线性Moore-Gibson-Thompson方程解的爆破研究  

On the Blow-up of Solutions to the Semilinear Moore-Gibson-Thompson Equation with a Nonlinear Memory Term

作　　者：欧阳柏平 侯春娟 OUYANG Baiping;HOU Chunjuan(College 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,广州511300

出　　处：《华南师范大学学报（自然科学版）》2022年第2期108-114,共7页Journal of South China Normal University(Natural Science Edition)

基　　金：广东省基础与应用基础研究基金省市联合基金项目(2021A1515111048);广东省普通高校重点项目(自然科学)(2019KZDXM042);广州华商学院校内项目(2020HSDS01)。

摘　　要：为了探讨记忆项对高阶波动方程爆破解的非局部影响,研究了具有非线性记忆项的半线性Moore-Gibson-Thompson方程解的爆破问题:在次临界情况下,通过引入时变泛函,利用测试函数推出了该泛函的第一下界和下界序列。然后应用迭代和切片技巧证明了解的全局非存在性和生命跨度上界估计。In order to explore the nonlocal impact of memory terms on the blow-up solutions to high-order wave equations,the blow-up of solutions to the Moore-Gibson-Thompson equation with a nonlinear memory term is studied.With the time-dependent functional and the test function,the first lower bound and lower bound series of the functional are derived.Then,the nonexistence of solutions and the upper bound estimate of solutions for the lifespan are proved by applying iteration and slicing technique.

关 键 词：非线性记忆项 Moore-Gibson-Thompson方程 爆破 

分 类 号：O175.4[理学—数学]