中北大学学报（自然科学版）2025，Vol.46Issue(1)：83-90,8.DOI:10.62756/jnuc.issn.1673-3193.2023.04.0027
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
摘要
Abstract
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 non-linear 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 addi-tion,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 solu-tions 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Key words
coupled wave equations/power memory terms/iteration method/blow-up/lifespan estimate分类
数理科学引用本文复制引用
王嘉兴,明森,韩伟,任翠..带幂次记忆项的波动方程耦合系统解的破裂[J].中北大学学报（自然科学版）,2025,46(1):83-90,8.基金项目
山西省基础研究计划资助项目(20210302123045,20210302123021,20210302123182) （20210302123045,20210302123021,20210302123182）
