非线性高阶波动型方程的局部解及解的Blow-up  

Local Existence and Blow-up of Solution for Nonlinear Higher-order Wave Equation

作　　者：叶耀军[1] YE Yaojun(Department of Mathematical Information and Statistics,Zhejiang University of Science and Technology,Hangzhou 310023,China)

机构地区：[1]浙江科技学院数学信息与统计系,杭州310023

出　　处：《应用数学学报》2021年第3期393-406,共14页Acta Mathematicae Applicatae Sinica

基　　金：浙江省自然科学基金(No.LY17A010009)资助项目.

摘　　要：本文研究了一类非线性高阶波动型方程的初边值问题.在阻尼项和源项的适当假设条件下,讨论了此问题局部解的存在唯一性.同时证明了初始能量为负时,解在有限时间内发生blow-up,并给出了解的生命区间估计.The initial boundary value problem for some nonlinear higher-order wave equation with damping and source terms in a bounded domain is studied.The local existence and uniqueness of solution is discussed under appropriate assumptions.Meanwhile,we show that this solution blows up in finite time as the initial energy is negative,and give the lifespan estimation of solution.

关 键 词：非线性高阶波动型方程 初边值问题 阻尼项和源项 局部解 BLOW-UP 

分 类 号：O175.2[理学—数学]