一类波动方程耦合方程组解的破裂  

Blow-up of Solutions to a Coupled System of Wave Equations

作　　者：杜嘉仪 明森 杨婕 苏业芹 DU Jia-yi;MING Sen;YANG Jie;SU Ye-qin(Department of Mathematics,North University of China,Taiyuan 030051,China;Department of Computer Science and Technology,North University of China,Taiyuan 030051,China;Department of Securities and Futures,Southwestern University of Finance and Economics,Chengdu 611130,China)

机构地区：[1]中北大学数学系,山西太原030051 [2]中北大学大数据学院,山西太原030051 [3]西南财经大学证券与期货学院,四川成都611130

出　　处：《云南师范大学学报（自然科学版）》2022年第2期18-22,共5页Journal of Yunnan Normal University:Natural Sciences Edition

基　　金：山西省自然科学基金资助项目(201901D211276);山西省基础研究计划资助项目(20210302123045,20210302123021);中北大学理学院研究生创新科研基金资助项目(20210814);中北大学科研创新团队支持计划资助项目(TD201901).

摘　　要：在外区域上研究了一类二维非线性波动方程耦合方程组的初边值问题,其中非线性项为幂次型非线性项|v|^(p),|u|^(q).利用检验函数方法,证明了次临界和临界情形解的破裂性态及其生命跨度的上界估计.The paper is concerned with the initial boundary value problem for a coupled system of nonlinear wave equations on exterior domain in two space dimensions.Blow-up and upper bound lifespan estimate of solutions to the problem with power type nonlinearities|v|^(p),|u|^(q) are proved by employing test function method in the sub-critical and critical cases.

关 键 词：波动方程 耦合方程组 检验函数方法 破裂 生命跨度 

分 类 号：O175.29[理学—数学]