Abels, Helmut and Rauchecker, Maximilian and Wilke, Mathias (2020) Well-posedness and qualitative behaviour of the Mullins-Sekerka problem with ninety-degree angle boundary contact. MATHEMATISCHE ANNALEN. ISSN 0025-5831, 1432-1807
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We show local well-posedness for a Mullins-Sekerka system with ninety degree angle boundary contact. We will describe the motion of the moving interface by a height function over a fixed reference surface. Using the theory of maximal regularity together with a linearization of the equations and a localization argument we will prove well-posedness of the full nonlinear problem via the contraction mapping principle. Here one difficulty lies in choosing the right space for the Neumann trace of the height function and showing maximal L-p-L-q-regularity for the linear problem. In the second part we show that solutions starting close to certain equilibria exist globally in time, are stable, and converge to an equilibrium solution at an exponential rate.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | EXISTENCE; SPACES; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Petra Gürster |
| Date Deposited: | 09 Apr 2021 09:44 |
| Last Modified: | 09 Apr 2021 09:44 |
| URI: | https://pred.uni-regensburg.de/id/eprint/44511 |
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