一类非线性粘弹性Petrovsky方程柯西问题解的爆破  

Blow-up of solution to Cauchy problem for a nonlinear viscoelastic Petrovsky equation

作　　者：胡文燕 HU Wenyan(School of Mathematics, Jinzhong University, Jinzhong 030600, China)

机构地区：[1]晋中学院数学系,山西晋中030600

出　　处：《安徽大学学报（自然科学版）》2022年第2期16-21,共6页Journal of Anhui University(Natural Science Edition)

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：对于非线性粘弹性Petrovsky方程,已有的研究成果大都是在有界区域内进行的.文章将其解由有界区域转移到无界区域,考虑一类具有粘弹性和非线性源项的非线性Petrovsky方程的柯西问题.当初始能量为非正值、非负不增的松弛函数g在适当的条件下,证得了其柯西问题的解在有限时间内会爆破的结论.For a nonlinear viscoelastic Petrovsky equation,most of the existing research results were carried out in the bounded domain.This paper transfered its solution from the bounded domain to the unbounded domain.This paper considered a Cauchy problem for a Petrovsky equation with viscoelasticity and nonlinear source terms.If assuming that the relaxation function g was nonnegative nonincreasing and the initial energy was non-positive,the result showed that the solution blew up at a finite time.

关 键 词：Petrovsky方程 无界区域 粘弹性 初始能量 爆破 

分 类 号：O175.23[理学—数学]