一类非线性抛物方程解的熄灭

Extinction of Solutions for the Nonlinear Parabolic Equation

讨论了非线性抛物方程初边值问题ut=△u+λ|u|γ-1u-βup,(x,t)∈Ω×(0,+∞),u(x,t)|Ω×(0,+∞)=0,u(x,0)=u0(x),x∈Ω解的渐近性态,给出了解在有限时间熄灭的充分条件.

The extinction phenomena of solutions of initial-boundary value problem for a type of nonlinear parabolic equation {δu/δt=△u＋λ｜u｜^γ-1u-βu^p,（x,t）∈Ω×（0,＋∞） u（x＋t）｜δΩ×（0,＋∞）=0, u（x＋0）=u0（x）,x∈Ω is studied. A sufficient condition about tho extinction of solutions is given.