# Norbert Požár

ノルベルト・ポジャール- Assistant Professor (助教)

- Kanazawa University
- Faculty of Mathematics and Physics, Institute of Science and Engineering
- 金沢大学・理工研究域・数物科学系
- Office: Room 228, 自然科学5号館

# Norbert Pozar’s homepage

## Research

nonlinear partial differential equations · free boundary problems · homogenization · viscosity solutions · crystal growth · phase transitions · mathematical modeling

### Papers and preprints

- Singular limit of the porous medium equation with a drift
- with I. Kim, B. Woodhouse. To appear in Adv. Math. (arXiv)
- Approximation of general facets by regular facets with respect to anisotropic total variation energies and its application to the crystalline mean curvature flow
- with Y. Giga. To appear in Comm. Pure Appl. Math. (arXiv)
- Long-time behavior of the one-phase Stefan problem in periodic and random media
- with G. T. T. Vu. To appear in DCDS-S. (arXiv)
- A level set crystalline mean curvature flow of surfaces
- with Y. Giga. Adv. Differential Equations
**21**(2016), no. 7–8, 631–698. (article link) - Porous medium equation to Hele-Shaw flow with general initial density
- with I. Kim. Trans. AMS
**370**(2018), no.2, 873–909. (article link) - Homogenization of the Hele-Shaw problem in periodic spatiotemporal media
- Arch. Rational Mech. Anal.
**217**(2015), no. 1, 155–230 (article link) - Periodic total variation flow of non-divergence type in
*R*^{n} - with M.-H. Giga and Y. Giga. J. Math. Pures Appl.
**102**(2014), 203–233 (article link) - Anisotropic total variation flow of non-divergence type on a higher dimensional torus
- with M.-H. Giga and Y. Giga. Adv. Math. Sci. Appl.
**21**(2013), no. 1, 235–266 (arXiv) - Nonlinear elliptic-parabolic problems
- with I. Kim. Arch. Rational Mech. Anal.
**210**(2013), no. 3, 975–1020 (article link) - 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)

#### Proceedings and abstracts

- A level set approach to the crystalline mean curvature flow
- Extended abstract for an invited talk at the Applied Math Section, MSJ Spring Meeting 2017, Tokyo Metropolitan University.
- Viscosity solutions for the level set formulation of the crystalline mean curvature flow
- RIMS Symposium on “Developments of the theory of evolution equations as the applications to the analysis for nonlinear phenomena” (Kyoto, October 2015), ed.: Katsuyuki Ishii, RIMS Kôkyûroku (2016), No. 1997, 16–31. article link

#### Others

- Selected properties of stationary axially symmetric fields in general relativity
- Master’s thesis (Charles University in Prague, Faculty of Mathematics and Physics)

### 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

- Finite element method for Laplace’s/Poisson’s equation in two dimensions
- notes on FEM
- Viscosity solutions for the porous medium equation
- old notes
- For students
- simple guides for various programming tools

## Teaching

## Links

### 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 well-formed structured HTML pages with included math formulas (supports MathJax)
- Inkscape – great vector drawing program, supports automatic export of images to
`.pdf`

,`.ps`

,`.dvi`

with labels stored in LaTeX `latex-flatten`

– Python script for flattening LaTeX files by inlining included files.

### Other

- GLOBAL COLORS Kanazawa グローバル・カラーズ・金沢 – English school