On the cauchy problem for a degenerate parabolic equation

Existence and uniqueness of global positive solutions to the degenerate par abolic problem ut = f(u)Deltau- in Rn x (0, infinity)} u\(t=0) = u(0) with f is an element of C-o ([0, infinity)) boolean AND C-1 ((0, infinity)) satisfying f (0) = 0 and f (s) > 0 for s > 0 are investigated. It is prove d that, without any further conditions on f, decay of u(o) in space implies uniform zero convergence of u(t) as t --> infinity. Furthermore, for a cer tain class of functions f explicit decay rates are established.