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FJ-LMI Seminar
Seminar information archive ～04/30｜Next seminar｜Future seminars 05/01～
| Organizer(s) | Toshiyuki Kobayashi, Michael Pevzner |
|---|
2024/01/30
16:30-17:30 Room # (Graduate School of Math. Sci. Bldg.)
Danielle HILHORST (CNRS, Université de Paris-Saclay, France)
Convergence of solutions of a one-phase Stefan problem with Neumann boundary data to a self-similar profile (英語)
https://fj-lmi.cnrs.fr/seminars/
Danielle HILHORST (CNRS, Université de Paris-Saclay, France)
Convergence of solutions of a one-phase Stefan problem with Neumann boundary data to a self-similar profile (英語)
[ Abstract ]
We study a one-dimensional one-phase Stefan problem with a Neumann boundary condition on the fixed part of the boundary.
We construct a unique self-similar solution and show that for a large class of initial data, the solution of the time evolution problem
converges to this self-similar solution as time tends to infinity. Similar results were already obtained by Bouguezzi, Hilhorst,
Miyamoto, and Scheid in the case of Dirichlet data on the fixed boundary. However, they had to show that the space derivative
of the solution uniformly converges to its limit. Here, our proof requires less regularity, which should make our arguments easier
to adapt to different settings.
This is a joint work with Sabrina Roscani and Piotr Rybka.
[ Reference URL ]We study a one-dimensional one-phase Stefan problem with a Neumann boundary condition on the fixed part of the boundary.
We construct a unique self-similar solution and show that for a large class of initial data, the solution of the time evolution problem
converges to this self-similar solution as time tends to infinity. Similar results were already obtained by Bouguezzi, Hilhorst,
Miyamoto, and Scheid in the case of Dirichlet data on the fixed boundary. However, they had to show that the space derivative
of the solution uniformly converges to its limit. Here, our proof requires less regularity, which should make our arguments easier
to adapt to different settings.
This is a joint work with Sabrina Roscani and Piotr Rybka.
https://fj-lmi.cnrs.fr/seminars/
