一类具超临界源的非线性黏弹性双曲方程解的爆破时间下界估计  

Estimate of a Lower Bound of Blow-Up Time for Solutions to a Class of Nonlinear Viscoelastic Hyperbolic Equations with Supercritical Sources

作　　者：曹春玲[1] 李行 李雨桐 蔡华[1] CAO Chunling;LI Hang;LI Yutong;CAI Hua(College of Mathematics,Jilin University,Changchun 130012,China;Yangxin Power Supply Company,State Grid Shandong Electric Power Company,Yangxin 251800,Shandong Province,China;Gengdan Institute of Beijing University of Technology,Beijing 101301,China)

机构地区：[1]吉林大学数学学院,长春130012 [2]国网山东省电力公司阳信供电公司,山东阳信251800 [3]北京工业大学耿丹学院,北京101301

出　　处：《吉林大学学报（理学版）》2019年第2期324-326,共3页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11271154;41874135)

摘　　要：考虑一类涉及超临界源项的非线性黏弹性双曲方程解的爆破时间下界估计,通过构造带阻尼项的控制函数,利用能量估计方法和Sobolev嵌入定理,得到了该问题解爆破时间的显式下界估计.We considered estimate of a lower bound of blow-up time for solutions to a class of nonlinear viscoelastic hyperbolic equations involving supercritical source terms.By constructing the control function with damping term,using the mehtod of energy estimate and Sobolev embedding theorem,we obtained an explicit estimate of lower bound of the blow-up time for the solutions to the problem.

关 键 词：黏弹性双曲方程 能量估计法 下界估计 爆破时间 

分 类 号：O175.27[理学—数学]