一类高阶波动方程的整体解及指数衰减估计  

Global Existence and Exponential Decay of Solution for Some Higher-Order Wave Equation

作　　者：叶耀军[1] 胡月[1] 

机构地区：[1]浙江科技学院数学与信息科学系,杭州310023

出　　处：《数学物理学报（A辑）》2018年第1期110-121,共12页Acta Mathematica Scientia

基　　金：浙江省自然科学基金(LY17A010009);国家自然科学基金(61273016)~~

摘　　要：研究了一类具有强耗散项的非线性高阶波动方程的初边值问题.通过在Sobolev空间中定义稳定集证明了此问题整体解的存在性,并给出了解的指数衰减估计.同时得到了初始能量为正时,解在不稳定集内发生爆破.This paper deals with the initial-boundary value problem for a class of higher-order nonlinear wave equation with strong dissipative term in a bounded domain. We prove the existence of global solutions for this problem by constructing a stable set in H0^m（Ω） and give the exponential decay estimate. Meanwhile, the blow-up result of solution in the unstable set is also obtained if the initial energy is positive.

关 键 词：非线性高阶波动方程 初边值问题 强耗散项 整体解 指数衰减 

分 类 号：O175.2[理学—数学]