STABILIZATION OF SOLUTIONS OF WEAKLY SINGULAR QUENCHING PROBLEMS

In this paper we prove that if 0 < beta < 1, D subset-of R(N) is bound ed, and lambda > 0, then every element of the omega-limit set of weak solutions of u(t) - DELTAu + lambdau(-beta)chi(u > 0) = 0 in D x [0, i nfinity), [GRAPHICS] is a weak stationary solution of this problem. A consequence of this is that if D is a ball, lambda is sufficiently sma ll, and u0 is a radial, then the set {(x, t)\u = 0} is a bounded subse t of D x [0, infinity).