Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6891964 | Computers & Mathematics with Applications | 2018 | 12 Pages |
Abstract
In this paper, we study the nonlocal nonlinear evolution equation CD0|tαu(t,x)â(Jâ|u|â|u|)(t,x)+CD0|tβu(t,x)=|u(t,x)|p,t>0,xâRd,where 1<α<2, 0<β<1, p>1, J:RdâR+, â is the convolution product in Rd, and CD0|tq, qâ{α,β}, is the Caputo left-sided fractional derivative of order q with respect to the time t. We prove that the problem admits no global weak solution other than the trivial one with suitable initial data when 1
0,xâRd,CD0|tαv(t,x)â(Jâ|v|â|v|)(t,x)+CD0|tβv(t,x)=|u(t,x)|q,t>0,xâRd,where 1<α<2, 0<β<1, p>1, and q>1. We prove that the system admitsnon global weak solution other than the trivial one with suitable initial data when 1
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Mohamed Jleli, Mokhtar Kirane, Bessem Samet,