摘要
考虑如下具有记忆项的非线性Petrovsky方程:utt+Δ~2u-∫t0g(t-τ)Δ~2 u(x,τ)dτ+︱u_t︱^(q-2) ut=︱u︱^( p-2) u,具Dirichlet边界条件的初边值问题。当松弛函数g满足适当的条件时,该问题的解在有限时间内会爆破。进一步对解的爆破时间进行研究,给出了正的初始能量下解的爆破时间的下界估计。
In this paper, we consider the initial boundary value problem with Dirichlet boundary conditions for the fol- lowing nonlinear Petrovsky equation with a memory term：utt＋Δ2 u-∫t0g（t-τ）Δ2 u（x,τ）dτ＋utq-2 ut=u p-2 u, Under some certain conditions of function g,the solution of the problem blows up in a finite time. We complete the results by studying the lower bounds for the blow-up time of the blow-up solutions.
出处
《山东科技大学学报（自然科学版）》
CAS
2017年第3期91-95,共5页
Journal of Shandong University of Science and Technology(Natural Science)
基金
国家自然科学基金项目(11171195)
