带有强阻尼时滞项的m-Laplacian型波方程解的爆破  

Blow-up of Solutions to the m-Laplacian Type Wave Equation with Strong Delay Terms

作　　者：高云龙 林荣瑞 佘连兵[1] 李爱静 GAO Yunlong;LIN Rongrui;SHE Lianbing;LI Aijing(School of Mathematics and Information Engineering,Liupanshui Normal University,Liupanshui 553004,China)

机构地区：[1]六盘水师范学院数学与计算机科学学院,六盘水553004

出　　处：《华南师范大学学报（自然科学版）》2021年第1期94-99,共6页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11571283);贵州省教育厅自然基金项目(黔教合KY字[2019]139,黔教合KY字[2019]143);六盘水师范学院校级项目(LPSSYKYJJ201801,LPSSKJTD201907)。

摘　　要：研究带有强阻尼时滞项的m-Laplacian型波方程:u tt-Δmu-Δu+gΔu-μ1Δu t(x,t)-μ2Δu t(x,t-τ)=u p-2 u解的爆破:当初始能量0<E(0)<E 1时,利用能量函数构造凹函数L 1(t),得到微分不等式d L 1(t)/d t≥ξ0L 1+ν1(t)(ξ0>0,ν>0,t≥0),在(0,t)上对此微分不等式积分,从而可知存在有限时间T*>0,使得当时间t趋于T*时,该m-Laplacian型波方程的解爆破;当初始能量E(0)<0时,构造凹函数L 2(t),通过同样的方法得到该方程的解存在有限时间爆破.Blow-up of solutions to the m-Laplacian type wave equation with strong delay was studied:u tt-Δmu-Δu+gΔu-μ1Δu t(x,t)-μ2Δu t(x,t-τ)=u p-2 u.When the initial energy 0<E(0)<E 1,the concave function L 1(t)was constructed with the energy function,and the differential inequality d L 1(t)/d t≥ξL 1+ν1(t)(ξ0>0,ν>0,t≥0)was obtained.Then,the differential inequality was integrated in(0,t),and it was proved that there was a finite time T*>0,so that when the time t was tended to T*,the m-Laplacian type wave equation underwent blow-up of solutions.When the initial energy E(0)<0,a concave function L 2(t)was also constructed.With the same method,it was found that the solutions to the equation had a finite-time blow-up.

关 键 词：M-LAPLACIAN 强阻尼时滞项 爆破 

分 类 号：O175.2[理学—数学]