一类带对数非线性项的分数阶伪抛物方程的存在性与爆破

Existence and Blow-up for a Class of Fractional Pseudo-parabolic Equations with Logarithmic Nonlinearity

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.