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This is a web page of Masato Kimura.

Masato Kimura (Dr.Sci.)

Professor

Faculty of Mathematics and Physics,

Institute of Science and Engineering,

Kanazawa University

Kakuma, Kanazawa, 920-1192, JAPAN

Tel:+81-(0)76-264-6064, Fax:+81-(0)76-264-6065

mkimura(AT)se.kanazawa-u.ac.jp

Recent and past research interests

moving boundary problems (mean curvature flow, Hele-Shaw problem, Stefan problem etc.)

numerical analysis for PDE (FDM, FEM, BEM etc.)

singular perturbation for elliptic eigenvalue problems with large drift

crack problems in fracture mechanics

shape derivative and its application

bulk-surface system

inverse Cauchy transform of domains

pattern formation in reaction diffusion systems

mathematical analysis of particle methods

Curriculum Vitae

Education

March 1990 : finishing study of Mathematics at Faculty of Science, Kyoto University

March 1992 : finishing master course study of Mathematics at Research Institute for Mathematical Sciences, Kyoto University

March 1996 : getting a Doctor degree of Science at Kyoto University

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Employment

April 1993 - March 1994 : JSPS research fellowship young scientist

April 1994 - September 1996 : Research Associate at Osaka Kyoiku University

October 1996 - October 2001 : Lecturer at Faculty of Science, Hiroshima University

November 2001 - March 2011 : Associate Professor at Faculty of Mathematics, Kyushu University

April 2007 - March 2008 : Visiting researcher at Nečas Center for Mathematical Modeling (Czech Technical Univ. in Prague)

April 2011 - March 2013 : Associate Professor at Institute of Mathematics for Industry, Kyushu University

April 2013 - present : Professor at Faculty of Mathematics and Physics, Institute of Science and Engineering, Kanazawa University

List of publications

M. Kimura,

Boundary Element Methods for Crack Problems,

Boundary Element Methods (Eds. S. Kobayashi, N. Nishimura),

Proceedings of the IABEM Symposium (Kyoto, October, 1991),

Springer-Verlag,(1992), pp.176-183.

M. Kimura,

Accurate Numerical Scheme for the Flow by Curvature,

Applied Mathematics Letters, Vol.7 (1994), pp.69-73.

M. Kimura,

Asymptotic estimation for the condition numbers in BEM,

Numerische Mathematik, Vol.73 (1996), pp.209-233.

M. Kimura,

Numerical analysis of moving boundary problems using

the boundary tracking method,

Japan J. Indust. Appl. Math., Vol.14 (1997), pp.373-398.

M. Kimura,

Time local existence of a moving boundary of the Hele-Shaw

flow with suction,

Euro. J. Appl. Math., Vol.10 (2000), pp.581-605.

M. Kimura,

Shape derivative and linearization of moving boundary problems,

GAKUTO International Series, Mathematical Sciences and

Applications Vol.13 (2000), pp.167-179.

M. Kimura and H. Notsu,

A level set method using the signed distance function.

Japan J. Indust. Appl. Math. 19 (2002), No.3, pp.415-446.

M. Kimura,

Numerical analysis of moving boundary problems,

Sugaku Expositions, 15 (2002), No.1, pp.71-88.

K. Shirakawa and M. Kimura,

Stability analysis for Allen-Cahn type equation

associated with the total variation energy,

Nonlinear Analysis, Vol.60, No.2 (2005), pp.257-282.

M. Kimura and S. Nagata,

Precise asymptotic behaviour of the first eigenvalue of

Sturm-Liouville problems with large drift,

Trans. Japan Soc. Indust. Appl. Math. Vol.15, No.3

(2005) pp.209-220. (in Japanese)

M. Kimura and I. Wakano,

New mathematical approach to the energy release rate

in crack extension,

Trans. Japan Soc. Indust. Appl. Math. Vol.16, No.3

(2006) pp.345-358. (in Japanese)

M.Kimura, H.Komura, M.Mimura, H.Miyoshi, T.Takaishi, and D.Ueyama,

Adaptive mesh finite element method for pattern dynamics

in reaction-diffusion systems.

Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2005,

COE Lecture Note Vol.3, Faculty of Mathematics, Kyushu University

ISSN 1881-4042 (2006) pp.56-68.

T.Nishida, K.Sugihara and M.Kimura,

Stable marker-particle method for the Voronoi diagram in a flow field,

J. Comp. Appl. Math. Vol.202 (2007) pp.377-391.

M.Kimura, H.Komura, M.Mimura, H.Miyoshi, T.Takaishi, and D.Ueyama,

Quantitative study of adaptive mesh FEM with

localization index of pattern

Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2006,

COE Lecture Note Vol.6, Faculty of Mathematics, Kyushu University

ISSN 1881-4042 (2007) pp.114-136.

M. Bene\v{s}, R. Chabiniok, M. Kimura, and K. Mikula,

Nonlinear Gauss-Seidel scheme for Allen-Cahn type systems,

MAGIA 2007 Proceedings, Slovak University of Technology

in Bratislava, ISBN 978-80-227-2796-9, (2007) pp.29-35.

M. Bene\v{s}, M. Kimura, and S. Yazaki,

Analytical and numerical aspects on motion of polygonal curves

with constant area speed,

MAGIA 2007 Proceedings, Slovak University of Technology

in Bratislava, ISBN 978-80-227-2796-9, (2007) pp.127-141.

M.Kimura,

Shape derivative of minimum potential

energy: abstract theory and applications,

to appear in

Jind\v{r}ich Ne\v{c}as Center for Mathematical Modeling

Lecture notes Volume IV, Topics in Mathematical Modeling

(2008), pp.1-38.

M.Kimura,

Geometry of hypersurfaces and moving hypersurfaces

in R^m ---for the study of moving boundary problems---,

to appear in

Jind\v{r}ich Ne\v{c}as Center for Mathematical Modeling

Lecture notes Volume IV, Topics in Mathematical Modeling

(2008), pp.39-93.

M. Bene\v{s}, M. Kimura, P. Pau\v{s}, D. \v{S}ev\v{c}ovi\v{c},

T. Tsujikawa, and S. Yazaki,

Application of a curvature adjusted method in image segmentation,

Bulletin of the Institute of Mathematics, Academia Sinica,

New Series, vol.3, no. 4 (2008), pp.509-523.

T. Takaishi and M. Kimura,

Phase field model for mode III crack growth

in two dimensional elasticity,

Kybernetika vol.45, no.4 (2009), pp.605-614.

S. Jimbo, M. Kimura and H. Notsu,

Exponential decay phenomenon of the principal eigenvalue of

an elliptic operator with a large drift term of gradient type,

Asymtotic Analysis, vol.65 (2009), pp.103-123.

M. Bene\v{s}, M. Kimura and S. Yazaki,

Second order numerical scheme for motion of polygonal curves

with constant area speed,

Interfaces and Free Boundaries, vol.11, no.4 (2009), pp.515-536.

K. Ishijima and M. Kimura,

Truncation error analysis of finite difference formulae

in meshfree particle methods,

Trans. Japan Soc. Indust. Appl. Math. Vol.20, No.3

(2010) pp.165-182. (in Japanese)

M. Kimura and T. Takaishi,

Phase field models for crack propagation.

Theoretical and Applied Mechanics Japan,

Vol. 59 (2011) pp.85-90.

M. Kimura and I. Wakano,

Shape derivative of potential energy and energy

release rate in fracture mechanics,

Journal of Math-for-industry, Vol.3 (2011) A, pp.21-31.

M. Benes, S. Yazaki and M. Kimura,

Computational studies of non-local anisotropic Allen-Cahn equation,

Math. Bohem. Vol.136, No.4 (2011) pp.429-437.

K. Ohtsuka and M. Kimura,

Differentiability of potential energies with a parameter

and shape sensitivity analysis for nonlinear case:

the p-Poisson problem,

Japan J. Indust. Appl. Math., Vol.29, No.1

(2012), pp.23-35.

K. Abe and M. Kimura,

Vibration-fracture model

for one dimensional spring-mass system,

Journal of Math-for-Industry, Vol.5 (2013) A, pp.25-32.

M. Kimura, D. Tagami and S. Yazaki,

Polygonal Hele–Shaw problem with surface tension,

Interfaces and Free Boundaries, Vol.15 (2013) pp.77-93.

Masato Kimura and Hirofumi Notsu,

A mathematical model of fracture phenomena

on a spring-block system,

RIMS K\^{o}ky\^{u}roku Vol.1848,

Kyoto University (2013) pp.171-186.

Hideyuki Azegami, Kohji Ohtsuka and Masato Kimura,

Shape derivative of cost function for singular point:

Evaluation by the generalized J integral,

JSIAM Letters Vol.6 (2014) pp.29–32.

Masato Kimura and Takeshi Takaishi,

A phase field approach to mathematical modeling

of crack propagation,

In: A Mathematical Approach to Research

Problems of Science and Technology - Theoretical

Basis and Developments in Mathematical Modeling,

eds. Ryuei Nishii, et al., Springer (2014) pp.161-170.

H. Notsu and M. Kimura,

Symmetry and positive definiteness of the tensor-valued

spring constant derived from P1-FEM for the

equations of linear elasticity,

Networks and Heterogeneous Media, Vol.9, No.4 (2014),

pp.617-634.

Armanda I., M. Kimura, T. Takaishi and Maharani A. U.,

Numerical construction of energy-theoretic crack propagation

based on a localized Francfort-Marigo model,

Recent Development in Computational Science Vol.6,

Kanazawa e-Publishing (2015) pp.35-41

Maharani A. U., M. Kimura, H. Azegami, K. Ohtsuka, and Armanda I.:

Shape optimization approach to a free boundary problem.

Recent Development in Computational Science Vol.6,

Kanazawa e-Publishing (2015) pp.42-55

V. Chalupeck\'y and M. Kimura:

An energy-consistent model of dislocation dynamics in an elastic body.

Mathematical Challenges in a New Phase of Materials Science

(Eds. Y. Nishiura and M. Kotani), Springer (2016) pp.53-68.

K. Ishii and M. Kimura:

Convergence of a threshold-type algorithm using the signed distance function.

Interfaces Free Boundaries, Vol.18 (2016) pp.479-522.

S. Shioda, A. U. Maharani, M. Kimura, H. Azegami, and K. Ohtsuka:

Shape optimization approach by traction method to inverse free boundary problems.

Mathematical Analysis of Continuum Mechanics and Industrial Applications

(Eds. H. Itou, et al.), Springer (2017) pp.111-123.

M. Kimura, H. Notsu, Y. Tanaka, and H. Yamamoto:

The gradient flow structure of an extended Maxwell viscoelastic model

and a structure-preserving finite element scheme.

Journal of Scientific Computing, (2018).

doi:10.1007/s10915-018-0799-2

(arXiv:1802.05566[math.NA])

G. Akagi and M. Kimura:

Unidirectional evolution equations of diffusion type.

J. Differential Equations, Vol.266 (2019) pp.1–43.

J. Minarčík, M. Kimura, and M. Beneš:

Comparing motion of curves and hypersurfaces in $\mathbb{R}^m$.

To appear in DCDS-B.

M. Kimura and A. Suzuki:

Deformation problem for glued elastic bodies

and an alternative iteration method.

To appear in Proceedings of CoMFoS18, Springer.

Talks in international conferences

Boundary Element Methods for Crack Problems,

Symposium of the International Association for Boundary

Element Methods: IBEM-91 (Kyoto, Japan), Octorber 1991.

Uniform Convergence of Numerical Solutions for an Integral

Equation of the First Kind appearing in BEM,

Japan-Russia joint seminar, Integral Equations in the Problems

of Mathematical Physics (Khabarovsk, Russia) June-July 1992.

On the Inverse Cauchy Transform Using the Variational Inequality,

Numerical Analysis for Elasticity and Related Topics

(Kyoto, Japan) July 1994.

On an Explicit Formula of the Inverse Cauchy Transform,

Japan-Russia Joint Workshop, Inverse Problems and Il-posed Problems

(Tokyo, Japan) September 1994.

Inverse Cauchy Transform of Domains,

"The Carleman Estimate and Inverse Problems"

(Kyoto, Japan) May 1995.

Time Local Existence of the Moving Boundary of the Hele-Shaw Flow

with Suction,

ESP-FBP Workshop ``Phase Transitions and Surface Tension"

(Weierstrass Institute for Applied Analysis and Stochastics, Berlin),

September 1996.

Convergence of a Boundary Tracking Method for the Curve Shortening Problem,

"Computation of Free Boundaries and Optimal Shapes" (Lamoura, France),

September 1996.

A level set method and its applicability and reliability,

The fifth China-Japan Joint Seminar on Numerical Mathematics

(Shanghai, China), August 2000.

A level set method and its applicability and reliability,

Interphase VIII. Workshop on Numerical Methods for Free

Boundary Problems (Berlin, Germany), Octorber 2000.

A level set method for moving boundary problems,

International Conference on Recent Advances in Computational

Mathematics (ICRACM 2001), (Matsuyama, Japan) ，Octorber 2001.

Variational mathematical model to quasi-stationary phase

transition with the Gibbs-Thomson effect,

Czech-Japanese Seminar in Applied Mathematics

(Prague, Czech Republic), August 2004.

On a geometric variational problem related to the

quasi-stationary Stefan-Gibbs-Thomson problem,

Workshop on Mathematical and Numerical Analysis of

Nonlinear Phenomena (Tokyo Metropolitan University),

February 2005.

Adaptive mesh FEM for pattern formation in reaction

diffusion systems,

2005 International Conference on Scientific Computation and

Differential Equations (SciCADE05),（Nagoya, Japan), May 2005.

Adaptive mesh finite element method for pattern formation,

The Second Czech-Japanese Seminar in Applied Mathematics,

(Kuju, Japan), September 2005.

Adaptive mesh finite element method for several pattern formations,

2005 Taiwan-Japan Joint Workshop on Numerical Analysis and

Scientific Computation, (Taipei, Taiwan), November 2005.

A quantitative study on adaptive FEM for several pattern formations,

Workshop on Numerical Analysis of Flow Problems

and Validated Computations, (Nagasaki, Japan), November 2005.

Mathematical study on the energy release rate in fracture mechanics,

First Slovak-Japan workshop on computational mathematics,

(Bratislava, Slovakia), September 2006.

Exponential decay of the first eigenvalue of an elliptic problem

with large drift,

Czech-Japanese seminar in applied mathematics 2006

(Prague, Czech Republic), September 2006.

Mathematical formulation of the energy derivatives in crack evolution,

Inernational Symposium " Understanding of Complex Pattern Dynamics "

(Kobe, Japan), September 2006.

Energy release rate in crack evolution of brittle fracture,

Matematika na vysokychskolach (Herbertov, Czech Republic) September 2007.

Convergence of nonlinear Gauss-Seidel scheme for Allen-Cahn type systems,

Slovak-Austrian Mathematical Congress (Podbanske, Slovakia) September 2007.

Crystalline motion in Hele-Shaw cell,

DMHF2007 : COE Conference on the Development of Dynamic Mathematics

with High Functionality

(Kyushu University, Japan) October 2007.

Finite difference methods for Allen-Cahn/Cahn-Hilliard equations,

The Second China-Japan-Korea Conference on Numerical Mathematics

(Weihai, China) August 2008.

On some generalizations of polygonal motions,

Tutorial Lectures and International Workshop

“Singular Diffusion and Evolving Interfaces”

(Hokkaido University, Japan) August 2010.

On some generalizations of polygonal motions,

Czech-Japanese Seminar in Applied Mathematics 2010

(Czech Technical University, Czech Republic) September 2010.

Truncation error analysis for particle methods,

EASIAM2011

(Waseda University, Kitakyushu Campus) June 28, 2011

Energy gradient systems in fracture and dislocation dynamics,

CASA Colloquium

(Eindhoven University of Technology) September 7, 2011

Continuous and discretecrack propagation models with

energy gradient property,

Forum "Math-for-Industry" 2011 (FMI2011)

(University of Hawai'i) October 25, 2011

Gradient flow models in elasticity

--- crack and dislocation dynamics,

Workshop on Reliability

in Scientific Computing and Related Topics

(Saikai National Park Kujyukushima Visitor Center, Sasebo JAPAN)

November 25, 2011

A fracture model in spring-block system,

ALGORITMY 2012 Conference on Scientific Computing

(Vysoke Tatry, Podbanske, Slovakia)

September 9-14, 2012

Continuous and discrete crack propagation models

with energy gradient property,

Czech-Japanese Seminar in Applied Mathematics 2013

(Meiji University, Tokyo, Japan)

September 5-8, 2013

Polygonal Hele-Shaw problem with surface tension,

Workshop on Free Boundaries in Laplacian Growth

Phenomena and Related Topics

(Tohoku University, Sendai, Japan)

October 14-17, 2013

Variational structures of moving boundary problems

and their polygonal analogues,

International Workshop on Singularities in boundary value problems

(Tokyo University of Science, Tokyo, Japan)

January 10, 2014

Strong solution to irreversible diffusion equation

and application to crack propagation model,

8th European Conference on Elliptic and Parabolic Problems

(Gaeta, Italy)

May 26–30, 2014

An irreversible diffusion equation

and a phase field model of crack propagation,

The 10th AIMS Conference on Dynamical Systems,

Differential Equations and Applications

(Madrid, Spain)

July 7-11, 2014

A fracture model on spring-block system with energy gradient structure,

RIMS intenational conference:

Mathematical Challenge to a New Phase of Materials Science,

(Masukawa Hall, Kyoto University, Kyoto, Japan)

August 4-8, 2014

Unidirectional evolution equation of diffusion type

and application to a crack propagation model,

The 32nd Kyushu Symposium on Partial Differential Equations

(Nishijin Plaza, Kyushu University, Fukuoka, Japan)

January 28-30, 2015

An irreversible gradient flow and its application

to a crack propagation model,

ICIAM2015 (Beijing, China)

August 10-14, 2015

Shape optimization approach by traction method

to an inverse free boundary problem,

CoMFoS15 (Fukuoka, Japan)

November 16-18, 2015

Unidirectional gradient flow and its application

to a crack propagation model,

Variational Models of Fracture (Banff International Research Station, Canada)

May, 8-13, 2016

Applications of a phasefield model for crack propagation,

WCCM XII&APCOM VI (Seoul, Korea)

July, 24-29, 2016

Shape optimization approach to free boundary problems by traction method,

ICCOPT2016 (Tokyo, Japan)

August, 6-11, 2016

Phase field model for crack propagation and some applications,

Japan-Taiwan Joint Workshop on Numerical Analysis and Scientific Computation

November, 26-28, 2016 (Keynote speaker)

Generalized hexagonal crystalline motion with facet collision

and breaking and application to a snow flake model,

Emerging Developments in Interfaces and Free Boundaries

(Oberwolfach Research Institute for Mathematics, Germany)

January, 22-28, 2017

Analysis of unidirectional diffusion equation and its gradient flow structure.

The 42nd Sapporo Symposium on Partial Differential Equations, Hokkaido University,

August 8-10, 2017.

Hexagonal crystal growth model with singularities.

Free Boundary Problems and Nonlinear PDEs, Hokkaido University,

September 26-28, 2017.

Unidirectional diffusion equation and application to crack growth models.

Karlstad Applied Analysis Seminar, Karlstad University, November 22, 2017.

A phase field model for crack propagation and some applications.

Applied Analysis Seminar, Louisiana State University, March 5, 2018.

A delamination-vibration model and its finite element analysis.

CoMFoS18: Mathematical Analysis of Continuum Mechanics II, Kyoto, June 13-15, 2018.

Gradient flow structure of the Maxwell-Zener model for viscoelasticity.

The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications,

Taipei, July 5-9, 2018.

Snow crystal growth model with supersaturation of vapor.

Czech-Japanese Seminar in Applied Mathematics 2018, Noto, Japan, July 13-16, 2818.

Phase field modeling for crack propagation with irreversibility.

China-Japan Symposium on Defects and Cracks in 2018 CSIAM Annual Meeting

Chengdu, China, September 14-16, 2018.

A structure preserving finite element method for Maxwell type viscoelasticity problem.

Japan-Taiwan Joint Workshop on Scientific Computation and Related Topics,

Taipei, November 24-26, 2018.