一类高阶波动方程的整体解及指数衰减估计

数学物理学报 ›› 2018, Vol. 38 ›› Issue (1): 110-121.

一类高阶波动方程的整体解及指数衰减估计

叶耀军, 胡月

浙江科技学院数学与信息科学系杭州 310023

收稿日期:2016-03-08 修回日期:2017-04-17 出版日期:2018-02-26 发布日期:2018-02-26
作者简介:叶耀军,yjye2013@163.com
基金资助:
浙江省自然科学基金（LY17A010009）和国家自然科学基金（61273016）

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

Ye Yaojun, Hu Yue

Department of Mathematics and Information Science, Zhejiang University of Science and Technology, Hangzhou 310023

Received:2016-03-08 Revised:2017-04-17 Online:2018-02-26 Published:2018-02-26
Supported by:
Supported by the Natural Science Foundation of Zhejiang Province (LY17A010009) and the NSFC (61273016)

摘要/Abstract

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.

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

Abstract: 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.

Key words: Nonlinear higher-order wave equation, Initial-boundary value problem, Strong dissipative term, Global solution, Exponential decay

中图分类号:

O175.2

叶耀军, 胡月. 一类高阶波动方程的整体解及指数衰减估计[J]. 数学物理学报, 2018, 38(1): 110-121.

Ye Yaojun, Hu Yue. Global Existence and Exponential Decay of Solution for Some Higher-Order Wave Equation[J]. Acta mathematica scientia,Series A, 2018, 38(1): 110-121.

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