Norbert Požár

ノルベルト・ポジャール Norbert Požár

Norbert Pozar’s homepage

Research

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

Curriculum Vitae

Papers and preprints

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, submitted. 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. To appear in Trans. AMS. arXiv
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)
Selected properties of stationary axially symmetric fields in general relativity
Master’s thesis (Charles University in Prague, Faculty of Mathematics and Physics)

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

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