一类具有导数型非线性记忆项的半线性双波动方程解的爆破研究  

Blow-up Study on Solutions to a Class of Semilinear Double-wave Equation with a Nonlinear Memory Term of Derivative Type

作　　者：欧阳柏平 肖胜中[2] 陈昌华 OUYANG Bai-ping;XIAO Sheng-zhong;CHEN Chang-hua(School of data Science,Guangzhou Huashang College,Guangzhou 511300,China;Industry and Commerce,Guangdong AIB Polytechnic College,Guangzhou 510507,China;Basic Course Department,GuangZhou Railway Polytechnic,Guangzhou 510430,China)

机构地区：[1]广州华商学院数据科学学院,广东广州511300 [2]广东农工商职业技术学院科研处,广东广州510507 [3]广州铁路职业技术学院基础课部,广东广州510430

出　　处：《数学的实践与认识》2022年第2期227-234,共8页Mathematics in Practice and Theory

基　　金：广东省普通高校创新团队项目(2020WCXTD008);广州华商学院项目(2020HSDS01,2021HSKT01);广州市哲学社会科学发展“十三五”规划课题(2019GZGJ209)。

摘　　要：研究了一类具有导数型非线性记忆项的半线性双波动方程在次临界情况下解的爆破问题.应用测试函数和泛函分析方法得到了其解的第一下界和迭代序列.然后运用迭代方法推出了其全局解的非存在性和生命跨度的上界估计.进一步补充了有关高阶波动方程柯西问题解的爆破研究.Blow-up problem for solutions of a semilinear double-wave equation with a nonlinear memory term of derivative type in.the subcritical case is investigated.By employing methods of test functions and functional analysis,the first lower bound and iterative series of solutions are obtained.Then,the nonexistence of global solutions and the upper bound estimate of the lifespan are derived via iteration arguments.Furthermore,it is a supplement to study on.blow-up of solutions to the Cauchy problem in high-order wave equations.

关 键 词：导数型非线性记忆项 半线性双波动方程 爆破 柯西问题 

分 类 号：O175[理学—数学]