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.
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