Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6892149 | Computers & Mathematics with Applications | 2018 | 14 Pages |
Abstract
In this paper, we consider the blow-up of solutions to a class of quasilinear reaction-diffusion problems g(u)t=ââ
Ï|âu|2âu+a(x)f(u) in ΩÃ(0,tâ),âuâν+γu=0 on âΩÃ(0,tâ),u(x,0)=u0(x) in Ω¯,where Ω is a bounded convex domain in Rn(nâ¥2), weighted nonlocal source satisfies a(x)f(u(x,t))â¤a1+a2u(x,t)pâ«Î©u(x,t)ldxm, and a1,a2,p,l, and m are positive constants. By utilizing a differential inequality technique and maximum principles, we establish conditions to guarantee that the solution remains global or blows up in a finite time. Moreover, an upper and a lower bound for blow-up time are derived. Furthermore, two examples are given to illustrate the applications of obtained results.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Juntang Ding, Xuhui Shen,