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Waiting time phenomena of the Hele-Shaw and the Stefan problem. (English) Zbl 1387.35629
Summary: 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.

35R35 Free boundary problems for PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
76D27 Other free boundary flows; Hele-Shaw flows
80A22 Stefan problems, phase changes, etc.
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