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Associate Professor POZAR Norbert
Faculty, Affiliation
Faculty of Mathematics and Physics, Institute of Science and Engineering
College and School Educational Field
Division of Mathematical and Physical Science, Graduate School of Natural Science and Technology
Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology
Course in Computational Science, School of Mathematics and Physics, College of Science and Engineering
Laboratory
Program in Applied Mathematics
Academic Background
【Academic background(Doctoral/Master's Degree)】
University of California, Los Angeles Doctor Department of Mathematics 2011
Charles University in Prague Master Faculty of Mathematics and Physics Mathematical and Computer Modelling in Physics and Technology 2006
【Degree】
Ph.D.
Career
Kanazawa University Associate Professor(2018/12/01-)
Kanazawa University Assistant Professor(2013/08/01-2018/11/30)
University of Tokyo Graduate School of Mathematical Sciences Project researcher(2011/09/01-2013/07/31)
Year & Month of Birth
Academic Society
The Mathematical Society of Japan
Award
Specialities
Mathematical analysis
Speciality Keywords
viscosity solutions, free boundary problems, crystalline mean curvature flow, porous medium equation, Hele-Shaw problem, Stefan problem
Research Themes
Level set method for the crystalline mean curvature flow
Homogenization of free boundary problems
Books
Papers
- On volume-preserving crystalline mean curvature flow I. Kim, D. Kwon, N. Pozar Mathematische Annalen 32pages 2021/10/21
- Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term Yoshikazu Giga, Norbert Pozar SN Partial Differential Equations and Applications 1 39 1-26 2020/10
- Singular limit of the porous medium equation with a drift Inwon Kim, Norbert Pozar, Brent Woodhouse Advances in Mathematics 349 682-732 2019/06/20
- An efficient numerical method for estimating the average free boundary velocity in an inhomogeneous Hele-Shaw problem Irma Palupi, Norbert Pozar The Science Reports of Kanazawa University 62 69-89 2019/04
- A numerical level set method for the Stefan problem with a crystalline Gibbs-Thomson law Norbert Pozar RIMS Kôkyûroku 2094 137-145 2018/11
- Long-time behavior of the one-phase Stefan problem in periodic and random media Norbert Pozar, Giang Thi Thu Vu Discrete & Continuous Dynamical Systems - Series S 11 5 991-1010 2018/10
- Approximation of General Facets by Regular Facets with Respect to Anisotropic Total Variation Energies and Its Application to Crystalline Mean Curvature Flow Yoshikazu Giga, Norbert Pozar Communications on Pure and Applied Mathematics 71 7 1461-1491 2018/04/10
- Porous medium equation to Hele-Shaw flow with general initial density Inwon Kim, Norbert Pozar Trans. Amer. Math. Soc. 370 2 873-909 2017/10/05
- Viscosity solutions for the level set formulation of the crystalline mean curvature flow Norbert Pozar RIMS Kôkyûroku 1997 16-31 2016/07
- A level set crystalline mean curvature flow of surfaces Yoshikazu Giga, Norbert Pozar Adv. Differential Equations 21 7/8 2016/05
- Homogenization of the Hele-Shaw Problem in Periodic Spatiotemporal Media Norbert Pozar Archive for Rational Mechanics and Analysis 217 1 155–230 2015/07
- Periodic total variation flow of non-divergence type in Rn Mi-Ho Giga, Yoshikazu Giga, Norbert Pozar Journal de Mathématiques Pures et Appliquées 102 1 203-233 2014/07
- Nonlinear elliptic-parabolic problems Inwon Kim, Norbert Pozar Archive for Rational Mechanics and Analysis 210 3 975–1020 2013/12
- Anisotropic total variation flow of non-divergence type on a higher dimensional torus Mi-Ho Giga, Yoshikazu Giga, Norbert Pozar Advances in Mathematical Sciences and Applications 21 1 235–266 2013
- Long-time behavior of a Hele-Shaw type problem in random media Norbert Pozar Interfaces and Free Boundaries 13 3 373-395 2011
- Viscosity Solutions for the Two-Phase Stefan Problem Inwon Kim, Norbert Pozar Communications in Partial Differential Equations 36 1 42-66 2010/11
- On convex comparison for exterior Bernoulli problems with discontinuous anisotropy William M Feldman, Norbert Pozar Interfaces and free boundaries 2024/07/22
- Discrete-to-continuum convergence of charged particles in 1D with annihilation P. van Meurs, M. A. Peletier, N. Pozar Archive for Rational Mechanics and Analysis 246 241-297 2022/09/06
- Motion by crystalline-like mean curvature: a survey Y. Giga, N. Pozar Bulletin of Mathematical Sciences 12 02 1-68 2022/07/13
Conference Presentations
- Level set method for the crystalline mean curvature flow with forcing(conference：Algorithmy 2024)(2024/03/24)
- A rate-independent model of droplet evolution(conference：Nonlinear analysis seminar)(2023/11/24)
- Forcing and volume constraint in the crystalline mean curvature flow(conference：Seminar on Partial Differential Equations)(2023/10/31)
- Continuum limit of dislocations with annihilation in one dimension(conference：Geometric PDEs and Applications )(2023/01/17)
- Crystalline mean curvature flow with a volume constraint(conference：Kyoto University, Dept. of Mathematics, Colloqium)(2021/07/07)
- Incompressible limit of the porous medium equation with a drift(2021/04/17)
- Forcing and volume constraint in the crystalline mean curvature flow(conference：2020 KMS Annual Meeting)(2020/10/24)
- Forcing in the crystalline mean curvature flow(conference：Surface and Interface Dynamics II)(2020/10/22)
- Self-similar solutions of the crystalline mean curvature flow(conference：Geometric Aspects of Solutions to Partial Differential Equations)(2019/06/12)
- Viscosity approach to the crystalline mean curvature flow and its applications(conference：Minisymposium "Singular parabolic equations and the motion of interfaces" at The 9th International Congress on Industrial and Applied Mathematics (ICIAM2019))(2019/07/19)
- Viscosity approach to the crystalline mean curvature flow(conference：Mini-symposium: Nonlinear Geometric Partial Differential Equations)(2020/02/06)
- Incompressible limit of the porous medium equation with a drift(conference：The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications)(2018/07/05)
- Viscosity solutions for the crystalline mean curvature flow(conference：BIRS Workshop 18w5033 - Advanced Developments for Surface and Interface Dynamics - Analysis and Computation)(2018/06/21)
- Large-time behavior of the anisotropic Stefan problem in nonuniform media(conference：The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications)(2018/07/09)
- A numerical level-set method for the Stefan problem with a crystalline Gibbs-Thomson law(2017/11/10)
- Singular limit of the porous medium equation with a drift(conference：Free Boundary Problems and Nonlinear PDEs)(2017/09/27)
- Crystalline curvature flow in three dimensions and the level set method(conference：界面現象の数理・モデリング研究合宿 2017)(2017/06/11)
- A level set approach to the crystalline mean curvature flow(conference：MSJ Spring Meeting 2017)(2017/03/26)
- A level set method for the crystalline mean curvature flow(conference：The 18th Northeastern Symposium on Mathematical Analysis)(2017/02/21)
- A level set method for the crystalline mean curvature flow(conference：Mathematical Aspects of Surface and Interface Dynamics 12)(2016/10/19)
- A level set approach to the crystalline mean curvature flow(conference：Anisotropy)(2016/09)
- A level set approach to the crystalline mean curvature flow of surfaces(conference：AIMS conference)(2016/07)
- Motion of surfaces by crystalline mean curvature: viscosity solutions approach(conference：Developments of the theory of evolution equations as applications of the analysis for nonlinear phenomena)(2015/10)
- Motion of surfaces by crystalline mean curvature: viscosity solutions approach(conference：The 8th International Congress on Industrial and Applied Mathematics (ICIAM2015))(2015/08)
- Homogenization of a Hele-Shaw-type problem in periodic spatiotemporal media(conference：Developments in the theory of Homogenization)(2015/07)
- A viscosity approach to motion of surfaces by crystalline mean curvature(conference：Viscosity solutions and related topics)(2015/03/27)
- Homogenization of a Hele-Shaw-type problem in periodic spatiotemporal media(conference：Workshop on Free Boundaries in Laplacian Growth Phenomena and Related Topics)(2013/10/14)
- A viscosity approach to total variation flows of non-divergence type(conference：Czech-Japanese Seminar in Applied Mathematics 2013)(2013/09/07)
- Homogenization of a Hele-Shaw-type problem in periodic time-dependent media(2013/03/08)
- Homogenization of a Hele-Shaw-type problem in periodic time-dependent media(conference：Weak KAM Theory and Related Topics)(2013/01/15)
Others
Arts and Fieldwork
Patent
Theme to the desired joint research
○Droplet dynamics
○Properties of the crystalline mean curvature flow
○Analysis of free boundary problems
Grant-in-Aid for Scientific Research
○「Toward applications of the crystalline mean curvature flow」(2023-2025)
○「Development of Viscosity and Variational Techniques for the Analysis of Moving Interfaces」(2018-2022)
○2024「エネルギー勾配流の新潮流：数学理論が開く多様な現象と応用の世界」(2020-2024)
○「Viscosity methods in homogenization of nonlinear PDEs」(2014-2017)
Competitive research funding,Contribution
Collaborative research,Consignment study
Classes (Bachelors)
○Programming for data science b(2022)
○Computational Science(2022)
○Programming for data science a(2022)
○Computational Science(2021)
○Introduction to Numerical Analysis 2b(2021)
○Introduction to Numerical Analysis 2a(2021)
○Introduction to Numerical Analysis 1a(2021)
○Introduction to Numerical Analysis 1b(2021)
○Selected Topics(2021)
○Selected Topics(2021)
○Introduction to Numerical Analysis 2b(2020)
○Introduction to Numerical Analysis 2a(2020)
○Selected Topics(2020)
○Selected Topics(2020)
○Computational Science(2020)
○Introduction to Numerical Analysis 2b(2019)
○Computational Science(2019)
○Introduction to Numerical Analysis 2a(2019)
○Mathematical Sciences 1(2019)
○Mathematical Sciences 1(2018)
○Community learning "Super" Experience Program(2017)
○Mathematical Sciences 1(2017)
○Introduction to Numerical Analysis 1(2016)
○Mathematical Sciences 1(2016)
Classes (Graduate Schools)
○Special topics in partial differential equations(2022)
○Special topics in partial differential equations(2022)
○Basics of Applied Analysis b(2022)
○Basics of Applied Analysis a(2022)
○Topics in Computational Science b(2022)
○Topics in Computational Science a(2022)
○Basics of Applied Analysis a(2021)
○Basics of Applied Analysis b(2021)
○Special topics in partial differential equations(2020)
○Special topics in partial differential equations(2020)
○Special topics in partial differential equations(2020)
○Special topics in partial differential equations(2020)
○Scientific Presentation A(2020)
○Scientific Presentation A(2020)
○Basics of Applied Analysis b(2020)
○Special Lectures on Computational Science(2020)
○Basics of Applied Analysis a(2020)
○Special topics in partial differential equations(2019)
○Special topics in partial differential equations(2019)
○Special topics in partial differential equations(2019)
○Special topics in partial differential equations(2019)
○Scientific Presentation A(2019)
○Scientific Presentation A(2019)
○Basics of Applied Analysis a(2019)
○Basics of Applied Analysis b(2019)
○Exercise A(2018)
○Basics of Applied Analysis b(2018)
○Lectures A for Foreign Students Ib(2018)
○Basics of Applied Analysis a(2018)
○Lectures A for Foreign Students Ia(2018)
○Seminar A(2018)
○Research Work A(2018)
○Topics in Computational Science a(2018)
○Lectures A for Foreign Students IIa(2018)
○Lectures A for Foreign Students IIb(2018)
○Topics in Computational Science b(2018)
○Seminar A(2017)
○Research Work A(2017)
○Lectures A for Foreign Students IIa(2017)
○Basics of Applied Analysis b(2017)
○Topics in Computational Science b(2017)
○Lectures A for Foreign Students IIb(2017)
○Topics in Computational Science a(2017)
○Exercise A(2017)
○Basics of Applied Analysis a(2017)
○Lectures A for Foreign Students Ib(2017)
○Lectures A for Foreign Students Ia(2017)
○Lectures A for Foreign Students Ib(2016)
○Basics of Applied Analysis a(2016)
○Analysis Ib(2016)
○Lectures A for Foreign Students IIa(2016)
○Topics in Computational Science a(2016)
○Topics in Computational Science b(2016)
○Lectures A for Foreign Students IIb(2016)
○Basics of Applied Analysis b(2016)
○Lectures A for Foreign Students Ia(2016)