TY - JOUR
T1 - The Stefan problem and concavity
AU - Chau, Albert
AU - Weinkove, Ben
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/10
Y1 - 2021/10
N2 - We construct examples for the one-phase Stefan problem which show that α-concavity of the solution is in general not preserved in time, for 0 ≤ α< 1 / 2. In particular, this shows that, in contrast to the case of the heat equation for a fixed convex domain, log concavity is not preserved for solutions of the Stefan problem.
AB - We construct examples for the one-phase Stefan problem which show that α-concavity of the solution is in general not preserved in time, for 0 ≤ α< 1 / 2. In particular, this shows that, in contrast to the case of the heat equation for a fixed convex domain, log concavity is not preserved for solutions of the Stefan problem.
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U2 - 10.1007/s00526-021-02061-y
DO - 10.1007/s00526-021-02061-y
M3 - Article
AN - SCOPUS:85111549816
SN - 0944-2669
VL - 60
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 5
M1 - 176
ER -