The Stefan problem and concavity

The Stefan problem and concavity

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 s...

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Veröffentlicht in:Calculus of variations and partial differential equations 2021-10, Vol.60 (5), Article 176
Hauptverfasser: Chau, Albert, Weinkove, Ben
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Calculus of Variations and Optimal Control
Optimization
Concavity
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
Thermodynamics
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Zusammenfassung: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.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-021-02061-y