ON OCCURRENCE OF COMPLETE BLOW-UP OF THE SOLUTION FOR A DEGENERATE SEMILINEAR PARABOLIC PROBLEM WITH INSULATED BOUNDARY CONDITIONS

Let a, σ, p, q, r, and m be constants with a > 0, σ > 0, p ≥ 0, q ≥ 0, r > 1, and m > 0. This article studies the following degenerate semilinear parabolic initial-boundary value problem, ξ quτ − uξξ = ξ pu r for 0 < ξ < a, 0 < τ < σ, u(ξ, 0) = u0 (ξ) = m for 0 ≤ ξ ≤ a, uξ(0, τ) = 0 = uξ(a, τ) for τ > 0. We derive criteria for u to blow up in finite time, and estimate the blow-up rate. We show that the blow-up is regional if q > p; the blow-up is complete if q = p; and the blow-up cannot be complete if p > q.