11 citations · 14 across the 6 of their papers we have counts for
12 papers
Critical Sets of Elliptic Equations with Rapidly Oscillating Coefficients in Two Dimensions
Fanghua Lin, Zhongwei Shen
In this paper we continue the study of critical sets of solutions $u_\e$ of second-order elliptic equations in divergence form with rapidly oscillating and periodic coefficients. I…
Matrix-valued Allen-Cahn equation and the Keller-Rubinstein-Sternberg problem
Mingwen Fei, Fanghua Lin, Wei Wang +1
In this paper, we consider the sharp interface limit of a matrix-valued Allen-Cahn equation, which takes the form: $$\partial_t A=ΔA-\varepsilon^{-2}( A A^{\mathrm{T}}A- A)~~\text{…
Isotropic-Nematic Phase Transition and Liquid Crystal Droplets
Fanghua Lin, Changyou Wang
Liquid crystal droplets are of great interest from physics and applications. Rigorous mathematical analysis is challenging as the problem involves harmonic maps (and in general the…
Upper bounds of nodal sets for eigenfunctions of eigenvalue problems
Fanghua Lin, Jiuyi Zhu
The aim of this article is to provide a simple and unified way to obtain the sharp upper bounds of nodal sets of eigenfunctions for different types of eigenvalue problems on real a…
Finite time blow-up for the nematic liquid crystal flow in dimension two
Chen-Chih Lai, Fanghua Lin, Changyou Wang +2
We consider the initial-boundary value problem of a simplified nematic liquid crystal flow in a bounded, smooth domain . Given any distinct points in the…
Harmonic maps in connection of phase transitions with higher dimensional potential wells
Fanghua Lin, Changyou Wang
This is in the sequel of authors' paper \cite{LPW} in which we had set up a program to verify rigorously some formal statements associated with the multiple component phase transit…