具任意高的正初始能量的非线性六阶波方程解的爆破  

Blow-up of Solution for Nonlinear Sixth-order Wave Equation with Arbitrarily High Positive Initial Energy

作　　者：郝江浩[1] 盖路路 HAO Jianghao;GE Lulu(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2020年第2期229-233,共5页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11871315,61374089);山西省应用基础研究(201801D121003)。

摘　　要：文章研究了带有源项的非线性六阶波方程的Cauchy问题具有任意高的正初始能量的解的爆破性质。通过给出关于初值的一类基本结构条件,利用泛函的符号不变性和凸性方法,证明了具有任意高的正初始能量解的爆破性质。We consider the Cauchy problem for a class of nonlinear sixth-order wave equation with source.Finite time blow-up of the solution at supercritical initial energy level are proved by the concave method and a new decomposition technical.Moreover,we present some general structural conditions on the initial data and by introducing some new functions,such that the solution blows up in finite time.

关 键 词：非线性六阶波方程 爆破 任意高的正初始能量 凸型方法 

分 类 号：O175[理学—数学]