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math.AP2019★ 5 cited
An existence theorem for Brakke flow with fixed boundary conditions
Salvatore Stuvard, Yoshihiro Tonegawa
Consider an arbitrary closed, countably -rectifiable set in a strictly convex -dimensional domain, and suppose that the set has finite -dimensional Hausdorff measure a…
math.AP2019★ 4 cited
A diffused interface with the advection term in a Sobolev space
Yoshihiro Tonegawa, Yuki Tsukamoto
We study the asymptotic limit of diffused surface energy in the van der Waals--Cahn--Hillard theory when an advection term is added and the energy is uniformly bounded. We prove th…