Blow-up analysis in quasilinear reaction-diffusion problems with weighted nonlocal source

In this paper, we consider the blow-up of solutions to a class of quasilinear reaction-diffusion problems g(u)t=∇⋅ρ|∇u|2∇u+a(x)f(u) in Ω×(0,t∗),∂u∂ν+γu=0 on ∂Ω×(0,t∗),u(x,0)=u0(x) in Ω¯,where Ω is a bounded convex domain in Rn(n≥2), weighted nonlocal source satisfies a(x)f(u(x,t))≤a1+a2u(x,t)p∫Ωu(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.