Papers and preprints

Homogenization of the Hele-Shaw problem in periodic spatiotemporal media

Submitted. arXiv

Periodic total variation flow of non-divergence type in Rⁿ

with M.-H. Giga and Y. Giga. Submitted. arXiv

Nonlinear elliptic-parabolic problems

with I. Kim. Submitted. arXiv

Long-time behavior of a Hele-Shaw type problem in random media

Interfaces Free Bound. 13 (2011), no. 3, 373–395. (article link)

Viscosity Solutions for the two-phase Stefan Problem

with I. Kim. Comm. Partial Differential Equations 36 (2011), no. 1, 42–66 (article link)

Selected properties of stationary axially symmetric fields in general relativity

Master’s thesis

Numerics

CrystalSolver

2D finite difference solver in Javascript running on GPU through WebGL (two-phase Stefan problem and total variation flow)

Two-phase Stefan problem with a mushy region

videos

Notes

Viscosity solutions for the porous medium equation

old notes

Useful math tools

• git – the fast version control system. Great tool when collaborating on a TeX document with multiple people, automatic version tracking, merging…
• pandoc – converter between many formats, in particular markdown, HTML and LaTeX. Easy to create structured well-formed HTML pages, include math formulas into HTML pages (supports MathJax).
• GNU make for Windows – automatization of the build process.
• Inkscape – great vector drawing program, supports automatic export of images to .pdf, .ps, .dvi with labels stored in LaTeX.