一类高阶非线性波动型方程整体解的存在性和指数衰减性  

Global Existence and Exponential Decay of Solutions for a Class of High-order Nonlinear Wave Equations

作　　者：王建平[1] 叶耀军[2] 叶子青 WANG Jian-ping;YE Yao-jun(College of Information and Management Science,Henan Agricultural University,Zhengzhou 450046,China;Department of Mathematics and Information Science,Zhejiang University of Science and Technology,Hangzhou 310023,China)

机构地区：[1]河南农业大学信息与管理科学学院,河南郑州450046 [2]浙江科技学院理学院,浙江杭州310023

出　　处：《数学的实践与认识》2019年第22期214-220,共7页Mathematics in Practice and Theory

基　　金：浙江省自然科学基金(LY17A010009);国家自然科学基金-河南人才培养联合基金(U1404102)

摘　　要：研究了一类带有阻尼和源项的高阶非线性波动方程utt+A+ut+aAut=b|u|^q-1u的初边值问题,这里A=(-△)^m,m≥1是一个自然数,a≥0,b>0和q>1是实数通过构造稳定集证明了这个问题整体解的存在,并应用乘子方法建立了整体解的指数衰减估计同时,在初始能量非负和a=0的条件下,得到了解在有限时间内发生爆破.A initial-boundary value problem for some nonlinear wave equation with damping and source terms utt+Au+ut+aAut=b|u|^q-1u in a bounded domain is studied,where A=(-△)^m,m≥1 is a nature numbera≥0,b>0 and g>1 are real numbers.The existence of global solutions for this problem is proved by constructing the stable setsand show the exponential decay estimate of global solutions as time goes to infinity by applying the multiplier method.Meanwhile,under the conditions of the nonnegative initial energy and a=0 it is showed that the solution blows up in finite time.

关 键 词：非线性波动方程 初边值问题 稳定集 非线性阻尼项和源项 指数衰减 

分 类 号：O17[理学—数学]