摘要
在n维空间中研究一类带散射阻尼项和记忆项的半线性波动方程的柯西问题。通过引入乘子处理阻尼项,构造检验函数,并且利用迭代方法,得到当非线性项指数满足一定条件时,问题的解会在有限时间内破裂,并给出解的生命跨度的上界估计。
This paper is concerned with the study of Cauchy problem for the nonlinear wave equation with scattering damping term and memory term for nspace dimensions.Blow-up of solution in finite time is proved under a certain assumption for the exponent in nonlinear term.By introducing a multiplier to deal with the damping term,constructing a test function and using iteration method,the author obtains upper bound lifespan estimate of solution for the problem.
作者
薛慧
明森
Xue Hui;Ming Sen(Shanxi Finance&Taxation College,Taiyuan 030024,China;North University of China,Taiyuan 030051,China)
出处
《廊坊师范学院学报（自然科学版）》
2024年第3期21-24,共4页
Journal of Langfang Normal University(Natural Science Edition)
基金
山西省基础研究计划资助项目(20210302123045、20210302123182)
中北大学本科教育教学改革项目(2021130)。
关键词
波动方程
记忆项
迭代方法
破裂
生命跨度估计
wave equation
memory term
iteration method
blow-up
lifespan estimate
