2024/04/23 by Tatsu‐Hiko Miura, Miura, Tatsu-Hiko · 3 citations
Engineering · Materials Science · Physics and Astronomy · #35B25 #35Q56 #35R01 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Thermal properties of materials
paper · pdf · doi:10.48550/arxiv.2404.14703
openalex publication_date 2024/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Ginzburg-Landau heat flow without magnetic effect in a curved thin domain under the Naumann boundary condition. When the curved thin domain shrinks to a given closed hypersurface as the thickness of the thin domain tends to zero, we show that the weighted average of a weak solution to the thin-domain problem converges weakly on the limit surface under the assumption that the initial data is of class L^∞ and satisfies some conditions. Moreover, under the same assumption, we derive a limit equation by characterizing the limit function as a weak solution, and prove a difference estimate on the limit surface of an averaged weak solution to the thin-domain problem and a weak solution to the limit problem explicitly in terms of the thickness of the thin domain. We also derive a difference estimate in the curved thin domain of weak solutions to the thin-domain problem and to the limit problem, but without requiring that the initial data of the thin-domain problem is of class L^∞.