Waiting time phenomena of the Hele-Shaw and the Stefan problem Sunhi ChoiInwon Kim 35K55viscosity solutionsfree boundary problemHele-Shaw problemStefan problemwaiting time phenomena In this paper we investigate the waiting time phenomena for the one-phase Hele-Shaw and Stefan problems. For the Hele-Shaw problem we identify a general criterion on the growth rate of the initial data. which determines the occurrence of a waiting time. For the Stefan problem we show that the waiting time phenomena depend on the balance between the initial data and the geometry of the initial positive phase. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2711 10.1512/iumj.2006.55.2711 en Indiana Univ. Math. J. 55 (2006) 525 - 552 state-of-the-art mathematics http://iumj.org/access/