摘要
本文研究了一类具有非线性耗散项的高阶Kirchhoff型方程的初边值问题.通过构造稳定集讨论了此问题整体解的存在性,应用Nakao的差分不等式建立了解能量的衰减估计.在初始能量为正的条件下,证明了解在有限时间内发生blow-up,并且给出了解的生命区间估计.
In this paper,the initial boundary value problem for some nonlinear higherorder Kirchhoff-type equation with damping and source terms in a bounded domain is studied.We prove the existence of global solutions for this problem by constructing a stable set and establish the energy decay estimate by applying a difference inequality due to Nakao.Meanwhile,under the condition of the positive initial energy,it is shown that the solution blows up in the finite time and the lifespan estimate of solution is also given.
作者
叶耀军
陶祥兴
Yao Jun YE;Xiang Xing TAO(Department of Mathematics and Information Science,Zhejiang University of Science and Technology,Hangzhou 310023,P.R.China)
出处
《数学学报（中文版）》
CSCD
北大核心
2019年第6期923-938,共16页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金(61273016,11171306,11571306)
浙江省自然科学基金(LY17A010009)
浙江省科技厅公益性技术应用研究课题资助项目(2015C33088)
