Norbert Požár
ノルベルト・ポジャール- Associate Professor (准教授)
- 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
Keywords: nonlinear partial differential equations · free boundary problems · homogenization · viscosity solutions · crystal growth · phase transitions · mathematical modeling
Papers and preprints
- On convex comparison for exterior Bernoulli problems with discontinuous anisotropy
- W. Feldman, N. Požár, To appear in Interfaces Free Bound. (arXiv)
- On the geometry of rate independent droplet evolution
- W. Feldman, I. Kim, N. Požár, submitted (arXiv)
- Motion by crystalline-like mean curvature: a survey
- Y. Giga, N. Požár, Bull. Math. Sci. 12 (2022), no. 02, 1–68 (article link, arXiv)
- On volume-preserving crystalline mean curvature flow
- I. Kim, D. Kwon, N. Požár, Math. Ann. 384 (2022), 1–42 (article link, arXiv)
- Discrete-to-continuum convergence of charged particles in 1D with annihilation
- P. van Meurs, M. A. Peletier, N. Pozar, Arch. Rational Mech. Anal. (2022), 241–297 (article link, arXiv)
- Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term
- Y. Giga, N. Požár, SN PDE Appl. 1 (2020), no. 39, 1–26 (article link, arXiv)
- An efficient numerical method for estimating the average free boundary velocity in an inhomogeneous Hele-Shaw problem
- I. Palupi, N. Požár, Sci. Rep. Kanazawa Univ. 62 (2018), 69–86 (arXiv)
- On the self-similar solutions of the crystalline mean curvature flow in three dimensions
- N. Požár, submitted (arXiv)
- Large-time behavior of one-phase Stefan-type problems with anisotropic diffusion in periodic media
- N. Požár, G.T.T. Vu, (arXiv)
- Singular limit of the porous medium equation with a drift
- I. Kim, N. Požár, B. Woodhouse, Adv. Math. 349 (2019), 682–732 (article link, 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
- Explicit viscosity solution of the crystalline curvature flow with fattening
- RIMS Symposium on “偏微分方程式の解の幾何的様相” (Kyoto, December 2019)
- 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