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Convexity of the free boundary in the Stefan problem and in the dam problem. (English) Zbl 0375.35028

MSC:
35K20 Initial-boundary value problems for second-order parabolic equations
35K05 Heat equation
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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[8] Friedman, A., A problem in hydraulics with non-monotone free boundary, Indiana Univ. Math. J., 25, 577-592 (1976). · Zbl 0321.35031 · doi:10.1512/iumj.1976.25.25046
[9] Friedman, A., Analyticity of the free boundary for the Stefan problem, Archive Rational Mech. Analysis., 61, 97-125 (1976). · Zbl 0329.35034
[10] Jensen, R, Smoothness of the free boundary in the Stefan problem with supercooled water, Ill. J. Math. to appear. · Zbl 0385.35033
[11] Jensen, R., Structure of the non-monotone free boundaries in a filtration problem, Indiana Univ. Math. J., to appear. · Zbl 0383.35027
[12] Shimborsky, E., Encadrement d’une frontiere libre relative a un probleme d’hydraulique, Bull. U.M.I., (4) 12, 66-67 (1975).
[13] van Meorbeke, P., An optimal stopping problem for linear reward, Acta Math., 132, 1-41 (1974). · Zbl 0277.30017 · doi:10.1007/BF02392106
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