THE EXTINCTION BEHAVIOR OF THE SOLUTIONS FOR A CLASS OF REACTION-DIFFUSION EQUATIONS

The methods of L p estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boudnary valuesu/t=Δu-λ|u| γ-1 u-βu ((x,t)∈Ω×(0,+∞)), u(x,t)| Ω×(0,+∞) =0, u(x,0)=u 0(x)∈H 1 0(Ω)∩L 1+γ (Ω) (x∈Ω).Sufficient and necessary conditions about the extinction of the solutions is given. Here λ>0, γ>0, β>0 are constants, Ω∈R N is bounded with smooth boundary Ω. At last, it is simulated with a higher order equation by using the present methods.