Extinction of solutions to a diffusion problem with nonlinear sources and variable density

Abstract

In this paper, we investigate the extinction of solutions to a diffusion problem with a variable density as follows, (0.1) ρ(x)ut=Δum+ρ(x)u∫Ωupdx(x,t)∈Ω×[0,T),u(x,t)=0(x,t)∈∂Ω×[0,T),u(x,0)=u0(x)x∈Ω.We give some sufficient conditions for the extinction of solutions of (0.1) by using the method of comparison principle and the integral estimates.

Keywords

• Extinction
• Variable density
• Comparison principle
• Nonlinear sources