一类带有记忆项的半线性波动方程解的爆破  

Blow-up of the Solution of A Class of Semilinear Wave Equation with Memory Term

作　　者：曹德刚 陈雪丽 杨晗[1] CAO De-gang;CHEN Xue-li;YANG Han(School of Mathematics,Southwest Jiaotong University,Chengdu Sichuan 611756,China)

机构地区：[1]西南交通大学数学学院,成都611756

出　　处：《西华师范大学学报（自然科学版）》2023年第5期490-495,共6页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11701477,11971394)。

摘　　要：本文研究一类带有记忆项的半线性波动方程的Cauchy问题。在初值具有紧支集条件下,利用Holder不等式和解的有限传播速度建立了能量解的估计以及相应泛函的下界估计。借助迭代技巧,当非线性项指数满足一定的条件时,证明了解的爆破,并估计了生命跨度的上界。This paper considers the Cauchy problems of a class of semilinear wave equations with nonlinear memory term.Under the condition that the initial value has compact supported sets,Holder inequality and the finite propagation speed of the solution are employed to establish the estimate of energy solution and the lower bound estimation of the corresponding functional.With the aid of iteration techniques,the blow-up of solution is proved and an upper bound of the lifespan is estimated under certain conditions of the nonlinear term exponent.

关 键 词：半线性波动方程 记忆项 迭代技巧 爆破 生命跨度 

分 类 号：O175.29[理学—数学]