Complete blow-up for degenerate semilinear parabolic equations

Let T less than or equal to infinity, a, q and x(0) be constants with a > 0, q greater than or equal to 0 and 0 < x(0) < a. Existence of a unique solution u is established for the following degenerate semilinear parabolic initial-boundary value problem: x(q)u(t) - u(xx) = f(u(x(0),t)), 0 < x < a, 0 < t < T, u(x,0) = u(0)(x) greater than or equal to 0, 0 less than or equal to x less than or equal to a, u(0,t) = u(a,t) = 0, 0 < t < T, where f and u(0) are given functions. We show that under certain conditions, u blows up in a finite time, and the set of blow-up points is the entire interval [0,a]. (C) 2000 Elsevier Science B.V. All rights reserved.