2019/04/30 by Yoshihiro Tonegawa, Yuki Tsukamoto
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advection #Bounded function #Curvature #Energy method #Geometric Analysis and Curvature Flows #Geometry #Limit (mathematics) #Mathematical analysis #Mathematics #Mean curvature #Nonlinear Partial Differential Equations #Physics #Quantum mechanics #Sobolev space #Space (punctuation) #Term (time) #math.AP #msc:49Q20 #van der Waals force
paper · pdf · doi:10.1007/s00526-020-01860-z
published as Calc. Var. 59, 184 (2020) · 23 pages
arxiv created 2020/08/02 · openalex publication_date 2020/10/09 · arxiv updated 2020/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract 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 that the limit interface is an integral varifold and the generalized mean curvature vector is determined by the advection term. As the application, a prescribed mean curvature problem is solved using the min–max method.