带双调和记忆项的四阶非线性伪抛物方程解的整体存在性和不存在性（英文）  

Global Existence and Nonexistence of Solutions for the Fourth-order Nonlinear Pseudo-parabolic Equation Involving the Bi-harmonic Memory Term

作　　者：龙群飞[1] 陈建青[1] LONG Qunfei CHEN Jianqing(School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian, 350108, P. R. China)

机构地区：[1]福建师范大学数学计算机科学学院,福州福建350108

出　　处：《数学进展》2017年第2期273-290,共18页Advances in Mathematics（China）

基　　金：Supported by NSFC(Youth Fund)(No.11401100),NSFC(No.11371091);the innovation group of "Nonlinear Analysis and Its Applications"(No.IRTL1206)

摘　　要：本文致力于带双调和记忆项的四阶非线性伪抛物方程初边值问题的研究.通过应用伽辽金方法、势井理论和相关估计,推导出了整体弱解的存在性.此外,通过应用凹性方法、势井理论和不稳定集的定义,不仅得到了具有非正初始能量(E(0)≤0)的弱解在有限时间爆破的结果,而且得到了具有正初始能量(0<E(0)<d_θ)的弱解在有限时间爆破的结果.In this paper, we are devoted to the study of the initial boundary value problem for the fourth-order nonlinear pseudo-parabolic equation with the bi-harmonic memory term. By applying the Galerkin method, potential well theory and related estimates, the existence of global weak solutions is derived. Moreover, not only the finite time blow-up of weak solutions with the non-positive initial energy （E（0）≤0） but also the finite time blow-up of weak solutions with the positive initial energy （0 〈 E（0） 〈 dθ） are obtained by applying concavity method, potential well theory and the definition of unstable set.

关 键 词：有限时间爆破 存在性问题 伪抛物方程 双调和记忆项 初边值问题 

分 类 号：O175.29[理学—数学]