New blow‐up criteria for a semilinear pseudo‐parabolic equation with general nonlinearity

Abstract

This paper is concerned with the blow-up phenomena for a semilinear pseudo-parabolic equation with general nonlinearity under the null Dirichlet boundary condition. When the nonlinearity satisfies a new structural condition, we obtain some new blow-up criteria with different initial energy levels and derive the growth estimations and life span of blow-up solutions.

Concavity Method: A concise survey

“…For the subcritical and critical initial energy cases, obtained a global existence, asymptotic behaviour and blowup phenomena in a finite time of the positive solution to the nonlinear porous medium equation. In [31], Li and Fang are concerned with the blowup phenomena for a semilinear pseudo-parabolic equation with general nonlinearity under the null Dirichlet boundary condition. When the nonlinearity satisfies a new structural condition, they obtain some new blowup criteria with different initial energy levels.…”

An overview of recent studies on the pseudo-parabolic equation

“…当考虑有界域上的半线性伪抛物方程的初边值问题时, Xu 和 Su [159] 利用位势井方法研究伪抛物 方程的工作引起了很大关注. 在此工作基础上, 人们相继建立了很多利用位势井方法讨论具有源项的 伪抛物方程 [59,89,96,98,100,169,170] 、变指标伪抛物方程 [92,113] 及退化、奇异伪抛物方程 [23,91] 解的渐近 行为的结果. 文献 [159] 首次通过初始能量的大小来划分如下伪抛物方程初边值问题解的整体存在和 爆破:…”