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）

发布时间：2018-07-11 19:02

  本文选题：有限时间爆破 + 存在性问题　； 参考：《数学进展》2017年02期

【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(0E(0)d_θ)的弱解在有限时间爆破的结果.
[Abstract]:This paper is devoted to the study of the initial and boundary value problems for fourth order nonlinear pseudoparabolic equations with biharmonic memory terms. By applying Galerkin method, potential well theory and correlation estimation, the existence of global weak solution is derived. In addition, by applying the concave method, the potential well theory and the definition of the unstable set, we not only obtain the results of the weak solution with non-positive initial energy (E (0) 鈮，

本文编号：2116308