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

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