吉林大学学报（理学版）2025，Vol.63Issue(6)：1533-1542,10.DOI:10.13413/j.cnki.jdxblxb.2025036
一类具卷积项和弱阻尼项的波动方程(组)全局解的不存在性
Nonexistence of Global Solutions to a Class of Wave Equations(Systems)with Convolution Terms and Weak Damping Terms
摘要
Abstract
By using the test function method,combining properties of the Heisenberg Laplace operator and K function,and utilizing relevant differential inequality techniques,we studied the rupture problem of the initial value problem solutions for a class of wave equations(systems)with convolution terms and weak damping terms in n-dimensional space.The results show that there is no global weak solution to the problem when the initial value satisfies certain assumptions.This obtained result gives the influence of parameters in the convolution term on rupture of the solution,and provided a reference for the study of existence of solutions to wave equations(systems)with weak damping and convolution type nonlinear terms in high dimensional spaces.关键词
弱阻尼波动方程/Heisenberg群/检验函数方法/破裂Key words
weakly damped wave equations/Heisenberg group/test function method/rupture分类
数学引用本文复制引用
李冬梅,明森,杜波..一类具卷积项和弱阻尼项的波动方程(组)全局解的不存在性[J].吉林大学学报（理学版）,2025,63(6):1533-1542,10.基金项目
山西省基础研究计划资助项目(批准号:20210302123045). （批准号:20210302123045）
