2019/07/26 by Harald Garcke, Garcke, Harald, Michael Gößwein +1
Materials Science · Mathematics · Physics and Astronomy · #35K52 #35K55 #35K93 #35R35 #53C44 #Analysis of PDEs (math.AP) #FOS: Mathematics #Solidification and crystal growth phenomena #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.AP #msc:35K52 #msc:35K55 #msc:35K93 #msc:35R35 #msc:53C44
paper · pdf · doi:10.48550/arxiv.1907.11682
openalex publication_date 2019/07/26 · arxiv created 2019/10/07 · arxiv updated 2019/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show short time existence for the evolution of triple junction clusters driven by the surface diffusion flow. On the triple line we use the boundary conditions derived by Garcke and Novick-Cohen as the singular limit of a Cahn-Hilliard equation with degenerated mobility. These conditions are concurrency of the triple junction, angle conditions between the hypersurfaces, continuity of the chemical potentials and a flux-balance. For the existence analysis we first write the geometric problem over a fixed reference surface and then use for the resulting analytic problem an approach in a parabolic Hölder setting.