带幂次记忆项的波动方程耦合系统解的破裂  

Blow‑Up of Solutions to Coupled System of Wave Equations with Power Memory Terms

作　　者：王嘉兴 明森 韩伟[1] 任翠 WANG Jiaxing;MING Sen;HAN Wei;REN Cui(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《中北大学学报(自然科学版)》2025年第1期83-90,共8页Journal of North University of China(Natural Science Edition)

基　　金：山西省基础研究计划资助项目(20210302123045,20210302123021,20210302123182)。

摘　　要：研究带阻尼项和非线性项的非线性波动方程解的破裂性态以及生命跨度,可以解释生活中不同形式的摩擦现象和非线性外力对波传播过程的影响。本文研究了n维空间中带散射阻尼项和幂次记忆项的波动方程耦合系统的Cauchy问题。首先,通过构造合适的乘子来克服散射阻尼项对波动方程的影响;其次,对幂次记忆项进行了放缩处理;最后,通过构造泛函,利用检验函数方法,以及构造迭代框架,得出小初值问题的解会在有限时间内破裂的结论,同时给出解的生命跨度的上界估计。本文将相关文献中带弱阻尼项的波动方程耦合系统推广为带散射阻尼项的波动方程耦合系统,将带幂次记忆项的单个波动方程推广为带幂次记忆项的波动方程耦合系统,推广了相关文献中带阻尼项和非线性项的单个波动方程解的破裂结果,并给出带阻尼项和非线性项的波动方程耦合系统解的生命跨度的上界估计。Studying the blow-up and lifespan estimate of the solution to nonlinear wave equations with damping term and nonlinear terms can explain the effects of different forms of friction phenomena and nonlinear external forces on wave propagation in daily life.This paper aims to investigate the Cauchy problem for coupled system of wave equations with scattering damping term and power memory terms in n space dimensions.Firstly,a suitable multiplier was constructed to overcome the influence of scattering damping term on wave equation.Secondly,the power memory terms were scaled down.Finally,by constructing functional,using test function method and constructing iterative framework,we obtained that the solutions of small initial value problem blow up in finite time,and the upper bound lifespan estimate of solutions was estimated.In this paper,the coupled system of wave equations with weak damping term in relevant literature was extended to the coupled system of wave equations with scattering damping term.In addition,the single wave equation with power memory term was extended to the coupled system of wave equations with power memory terms.It is generalized that the rupture results of single wave equation solutions with damping term and nonlinear terms in relevant literature.The upper bound lifespan estimation of solutions to coupled wave equation system with damping term and nonlinear terms was provided.

关 键 词：耦合波动方程 幂次记忆项 迭代方法 破裂 生命跨度估计 

分 类 号：O436[机械工程—光学工程]