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 Rn
- 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,.dviwith 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