摘要
研究了一类带对数非线性项的分数阶伪抛物方程的初边值问题.基于分数阶Sobolev空间理论,当初始能量J(u_(0))<d,I(u_(0))<0时,利用位势阱方法和对数不等式,得到了解的全局存在性.此外利用凹线法给出了初始能量J(u_(0))<d,I(u_(0))<0时有限时间爆破的充分条件.
In this paper, we consider the initial boundary value problem for a class of fractional pseudo-parabolic equations with logarithmic nonlinearity.Based on the theorems of fractional Sobolev spaces and by virtue of the potential well method and logarithmic inequality, the existence of global solutions are obtained under the initial energy J(u_(0))<d,I(u_(0))<0.In addition, sufficient conditions for finite time blow-up are obtained by using the concave method under the initial energy J(u_(0))<d,I(u_(0))<0.
作者
王冬秀
邓启刚
曾福庚
WANG Dongxiu;DENG Qigang;ZENG Fugeng(School of Date Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)
出处
《湖北民族大学学报(自然科学版)》
CAS
2022年第1期96-102,共7页
Journal of Hubei Minzu University:Natural Science Edition
基金
贵州省科技计划项目([2016]7075)。
关键词
伪抛物
存在性
爆破
分数阶
位势阱
pseudo-parabolic
existence
blow-up
fractional
potential wells