A FURTHER LOOK AT BLOW-UP PHENOMENA FOR U (T)-DELTA-U=G(U)

We are concerned with relations between the existence of global, class ical solutions of the evolution equation (1) and the existence of weak solutions of the stationary problem (2). Omega subset R(N) is a smoot h, bounded domain and g: 0, infinity) is a C-1 convex, nondecreasing function. We show that if there exists a weak solution of (2), then th ere exists a global, classical solution of (1). Conversely, if there e xists a global, classical solution of (1) and if integral infinity ds/ g (s) < infinity, then there exists a weak solution of (2).