一类具记忆项的非线性Petrovsky方程解的爆破  

Blow up of solutions for a nonlinear Petrovsky equation with memory term

作　　者：胡文燕[1] 杜晓英[1] HU Wen-yan;DU Xiao-ying(School of Mathematics,Jinzhong University,Jinzhong 030619,Shanxi,China)

机构地区：[1]晋中学院数学学院,山西晋中030619

出　　处：《西北师范大学学报（自然科学版）》2019年第1期16-19,25,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11171195);山西省教育科学"十三五"规划课题资助项目(GH-16107);晋中学院优秀教学团队资助项目

摘　　要：考虑一类非线性Petrovsky方程的具Dirichlet边界条件的初边值问题.在假设松弛函数g和初值u0,u1满足适当的条件,且初始能量为非正值时,利用能量法证得其解在有限时间内爆破.A nonlinear Petrovsky equation with initial conditions and Dirichlet boundary conditions is considered.Assuming that the relaxation function g satisfies the appropriate conditions and the initial energy is not positive,the energy method is used to prove that the solution blows up in finite time.

关 键 词：非线性Petrovsky方程 松弛函数 记忆项 初始能量 爆破 

分 类 号：O175.23[理学—数学]