On solutions of space-fractional diffusion equations by means of potential wells

Electronic Journal of Qualitative Theory of Differential Equations

卷:2016

Yongqiang Fu¹  Patrizia Pucci² 

[1] Harbin Institute of Technology, Harbin, P. R. China;

[2] University of Perugia, Perugia, Italy;

关键词: potential wells;    space-fractional wave equations;    global solutions;    fractional sobolev spaces;   

DOI  :  10.14232/ejqtde.2016.1.70

来源: DOAJ

【 摘 要 】

In this paper, we study the initial boundary value problem of space-fractional diffusion equations. First, we introduce a family of potential wells. Then we show the existence of global weak solutions, provided that the initial energy $J(u_0)$ is positive and less than the potential well depth $d$. Finally, we establish the vacuum isolating and blow up of strong solutions.

【 授权许可】

Unknown