An extinction delay mechanism for some evolution equations

Abstract

We study the ”finite extinction phenomenon”(there exists t0 ≥ 0 such that u(t, x) ≡ 0 ∀t ≥ t0, a.e. x ∈ Ω) for solutions of parabolic reaction-diffusion equations of the type ∂u ∂t − k∆u+λb(t)f(u(t − τ, x)) = 0 and ordinary delayed differential equations (k = 0) with a delay term τ > 0.