一类带记忆项的波动方程解的破裂
Blow-up of Solutions for a Class of Wave Equations with Memory Term
薛慧 1明森2
作者信息
- 1. 山西省财政税务专科学校,山西太原 030024
- 2. 中北大学,山西太原 030051
- 折叠
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.
Abstract
This paper is concerned with the study of Cauchy problem for the nonlinear wave equation with scattering damp-ing 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 us-ing iteration method,the author obtains upper bound lifespan estimate of solution for the problem.
关键词
波动方程/记忆项/迭代方法/破裂/生命跨度估计Key words
wave equation/memory term/iteration method/blow-up/lifespan estimate引用本文复制引用
基金项目
山西省基础研究计划资助项目(20210302123045)
山西省基础研究计划资助项目(20210302123182)
中北大学本科教育教学改革项目(2021130)
出版年
2024
NETL
NSTL
万方数据