Mediterranean Journal of Mathematics   2016 年 13 卷 5 期

2016.10.01

In this paper, the authors prove that the solution blows up in a finite time for a larger class of initial data, namely positive initial energy. The results generalize and improve that of Giacomoni et??al. (J Math Anal Appl 410:607??“624, 2014). Furthermore, a lower bound estimate about blow-up time is also established. Finally, two examples are given in the paper to show the existence of the initial datum satisfying the conditions in the main theorem.