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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.

MSC:
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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