一类强阻尼波动方程组的整体解及其爆破  

Global Solutions and Blow-up for Systems of Damped Wave Equations

作　　者：叶耀军[1] 李兰兰 YE Yaojun;LI Lanlan(School of Science,Zhejiang University of Science and Technology,Hangzhou,Zhejiang,310023,P.R.China)

机构地区：[1]浙江科技学院理学院,浙江杭州310023

出　　处：《数学进展》2022年第4期622-634,共13页Advances in Mathematics（China）

基　　金：浙江省自然科学基金(No.LY17A010009)。

摘　　要：本文研究一类具有强阻尼项的半线性波动方程组的初边值问题.应用位势井方法及一致有界连续性原理证明了整体解的存在性,通过引入适当的Lyapunov函数建立了整体解的指数衰减估计.同时,利用凹性方法在不稳定集中得到了解的爆破.The initial-boundary value problem for a class of semilinear wave equation systems with strong dissipative term in bounded domain is studied.The existence of global solutions for this problem is proved by using potential well method and the uniform bounded continuity principle,and the exponential decay of global solutions is established through introducing an appropriate Lyapunov function.Meanwhile,blow-up of solutions in the unstable set is also obtained by applying the concave method.

关 键 词：波动方程组 整体解 指数衰减性 爆破 

分 类 号：O175.2[理学—数学]