# 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

- An efficient numerical method for estimating the average free boundary velocity in an inhomogeneous Hele-Shaw problem
- I. Palupi, N. Požár, submitted ()
- On the self-similar solutions of the crystalline mean curvature flow in three dimensions
- N. Požár, (arXiv)
- Large-time behavior of one-phase Stefan-type problems with anisotropic diffusion in periodic media
- N. Požár, G.T.T. Vu, submitted (arXiv)
- Singular limit of the porous medium equation with a drift
- I. Kim, N. Požár, B. Woodhouse, To appear in Adv. Math. (arXiv)
- Long-time behavior of the one-phase Stefan problem in periodic and random media
- N. Požár, G.T.T. Vu, Discrete & Continuous Dynamical Systems - S
**11**(2018), no. 5, 991–1010 (article link, arXiv) - Approximation of General Facets by Regular Facets with Respect to Anisotropic Total Variation Energies and Its Application to Crystalline Mean Curvature Flow
- Y. Giga, N. Požár, Comm. Pure Appl. Math.
**71**(2018), no. 7, 1461–1491 (article link) - Porous medium equation to hele-shaw flow with general initial density
- I. Kim, N. Požár, Trans. AMS
**370**(2018), no. 2, 873–909 (article link) - A level set crystalline mean curvature flow of surfaces
- Y. Giga, N. Požár, Adv. Differential Equations
**21**(2016), no. 7-8, 631–698 (article link) - Homogenization of the Hele-Shaw Problem in Periodic Spatiotemporal Media
- N. Požár, Arch. Rational Mech. Anal.
**217**(2015), no. 1, 155–230 (article link) - Periodic total variation flow of non-divergence type in Rn
- M.-H. Giga, Y. Giga, N. Požár, J. Math. Pures Appl.
**102**(2014), no. 1, 203–233 (article link) - Anisotropic total variation flow of non-divergence type on a higher dimensional torus
- M.-H. Giga, Y. Giga, N. Požár, Adv. Math. Sci. Appl.
**23**(2013), no. 1, 235–266 (arXiv) - Nonlinear Elliptic-Parabolic Problems
- I.C. Kim, N. Požár, Arch. Rational Mech. Anal.
**210**(2013), no. 3, 975–1020 (article link) - Long-time behavior of a Hele-Shaw type problem in random media
- N. Požár, Interfaces Free Bound.
**13**(2011), no. 3, 373–395 (article link) - Viscosity solutions for the two-phase Stefan problem
- I.C. Kim, N. Požár, Comm. Partial Differential Equations
**36**(2011), no. 1, 42–66 (article link)

#### Proceedings and abstracts

- A numerical level set method for the Stefan problem with a crystalline Gibbs-Thomson law
- RIMS Symposium on “数値解析学の最前線 —理論・方法・応用—” (Kyoto, November 2017)
- 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)

### Talks

### 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
- A note on the basic math of fluid equations
- the change of variables formula
- 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