Please use this identifier to cite or link to this item:
Title: Well-posedness and qualitative behaviour of the Mullins-Sekerka problem with ninety-degree angle boundary contact
Author(s): Abels, HelmutLook up in the Integrated Authority File of the German National Library
Rauchecker, Maximilian
Wilke, MathiasLook up in the Integrated Authority File of the German National Library
Issue Date: 2021
Type: Article
Language: English
Abstract: 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 Lp−Lq-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.
Open Access: Open access publication
License: (CC BY 4.0) Creative Commons Attribution 4.0(CC BY 4.0) Creative Commons Attribution 4.0
Journal Title: Mathematische Annalen
Publisher: Springer
Publisher Place: Berlin
Volume: 381
Original Publication: 10.1007/s00208-020-02007-3
Page Start: 363
Page End: 403
Appears in Collections:Open Access Publikationen der MLU

Files in This Item:
File Description SizeFormat 
s00208-020-02007-3.pdf594.09 kBAdobe PDFThumbnail