一类带散射阻尼项的波动方程解的破裂  

Blow-up of Solutions to a Wave Equation with Scattering Damping Term

作　　者：杜嘉仪 明森 韩伟[1] 苏业芹 DU Jia-yi;MING Sen;HAN Wei;SU Ye-qin(School of Science, 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]中北大学理学院,山西太原030051 [2]西南财经大学证券与期货学院,四川成都611130

出　　处：《中北大学学报（自然科学版）》2021年第6期481-485,494,共6页Journal of North University of China(Natural Science 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);中北大学科研创新团队支持计划资助项目(TD201901);山西省高等学校优秀青年学术带头人支持计划资助项目;中北大学理学院2021年研究生创新科研项目(20210814)。

摘　　要：研究了外区域上一类带散射阻尼项的变系数波动方程的初边值问题.利用检验函数方法和迭代方法,分别得到带幂次非线性项|u|^(p),导数非线性项|ut|^(p)及组合非线性项|ut|^(p)+|u|^(q)的初边值问题解的破裂及其生命跨度的上界估计.This paper was devoted to investigating the initial boundary value problems of a variable coefficient wave equation with scattering damping term on exterior domain.Blow-up and upper bound lifespan estimates of solutions to the problems with power type nonlinearity|u|^(p),derivative type nonlinearity|ut|^(p) and combined type nonlinearities|ut|^(p)+|u|^(q) were derived respectively by applying test function method and iteration approach.

关 键 词：变系数波动方程 散射阻尼项 迭代方法 破裂 生命跨度 

分 类 号：O175.29[理学—数学]