English

A diffused interface with the advection term in a Sobolev space

Analysis of PDEs 2020-10-12 v2

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.

Keywords

Cite

@article{arxiv.1904.00525,
  title  = {A diffused interface with the advection term in a Sobolev space},
  author = {Yoshihiro Tonegawa and Yuki Tsukamoto},
  journal= {arXiv preprint arXiv:1904.00525},
  year   = {2020}
}

Comments

23 pages

R2 v1 2026-06-23T08:24:41.314Z