Resumen de Initial traces of solutions to a one-phase Stefan problem in an infinite strip.

D. Andreucci, M.K. Korten

• The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u Î L1loc (Rn x (0,T)) to (0.1) ut - ?(u - 1)+ = 0, in D'(Rn x (0,T)), for T > 0, n = 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection u is the enthalpy, (u - 1)+ the temperature, and u = 1 the critical temperature of change of phase. Our estimate may be written in the form (0.2) ?Rn u(x,t) e-|x|2 / (2 (T - t)) dx = C, 0 < t < T, where C depends on n, T, t, u but it stays bounded as T ? 0.