Publications
List of publications
Y. Aizawa and M. Kimura:
Universal Approximation Properties for ODENet and ResNet.
arXiv:2101.10229
M. Kimura, P. van Meurs, and Z.X. Yang:
Particle dynamics with elastic collision at the boundary: existence and partial uniqueness of solutions.
arXiv:2011.14485
P. Kow and M. Kimura:
The Lewy-Stampacchia Inequality for the Fractional Laplacian and Its Application to Anomalous Unidirectional Diffusion Equations.
arXiv:1909.00588
M. Negri and M. Kimura:
Weak solutions for gradient flows under monotonicity constraints.
arXiv:1908.10111
M. Kimura and P. van Meurs:
Quantitative estimate of the continuum approximations of interacting particle systems in one dimension.
SIAM J. Math. Anal., 53(1), (2021) pp.681–709.
https://doi.org/10.1137/20M1322054
arXiv:2002.11876
Md. M. Murshed, K. Futai, M. Kimura, and H. Notsu:
Theoretical and numerical studies for energy estimates
of the shallow water equations with a transmission boundary condition.
Discrete & Continuous Dynamical Systems-S (2021) 16 pages.
doi: 10.3934/dcdss.2020230
M. Kimura and P. van Meurs:
Regularity of the minimiser of one-dimensional interaction energies.
ESAIM: Control, Optimisation and Calculus of Variations Vol.26 (2020)
article number 27 (43 pages).
https://doi.org/10.1051/cocv/2019043
arXiv:1710.00282
M. Kimura and A. Suzuki:
Deformation problem for glued elastic bodies
and an alternative iteration method.
CoMFoS 2018: Mathematical Analysis of Continuum Mechanics
and Industrial Applications III,
Mathematics for Industry, Vol 34, Springer, Singapore (2020) pp 81-94.
https://doi.org/10.1007/978-981-15-6062-0_6（査読あり）
T. Taniguchi, N. Akashi, H. Notsu, M. Kimura, H. Tsukahara, K. Nakajima:
Chaos in nanomagnet via feedback current.
Phys. Rev. B Vol.100 (2019) 174425.
M. Kimura, K. Matsui, A. Muntean, H. Notsu:
Analysis of a projection method for the Stokes problem using an ε-Stokes approach.
Japan Journal of Industrial and Applied Mathematics Vol.36 (2019) pp.959–985.
DOI: 10.1007/s13160-019-00373-3
M. Kimura, P. van Meurs, Z.X. Yang:
Particle dynamics subject to impenetrable boundaries: existence
and uniqueness of mild solutions.
SIAM J. Math. Anal. Vol.51, No.6 (2019) pp.5049-5076.
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, Vol.78 (2019) pp.1111-1131.
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 $\mathbb{R}^m$.
DCDS-B., Vol.24, No.9 (2019) pp.4815-4826.
doi: 10.3934/dcdsb.2019032
I. Wijaya, M. Kimura, and H. Notsu:
A new Lagrange-Galerkin scheme for solving fluid flow in porous media.
Journal of Physics Conference Series 1245 (2019) 012007
doi:10.1088/1742-6596/1245/1/012007
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.
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.
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
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,
A Mathematical Approach to Research Problems of Science and Technology,
Series of Mathematics for Industry, Vol.5, 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.
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.
M. Kimura and H. Notsu,
A mathematical model of fracture phenomena on a spring-block system.
RIMS Kokyuroku, Vol.1848 (2013) pp.171-186.
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.
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,
Computatinon-local anisotropic Allen-Cahn equation,
Math. Bohem. Vol.136, No.4 (2011) pp.429-437.
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,
Asymptotic 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.
M.Kimura,
Shape derivative of minimum potential
energy: abstract theory and applications,
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---,
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.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, 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 Seminar3, Faculty of Mathematics, Kyushu University
ISSN 1881-4042 (2006) pp.56-68.
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 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.
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,
Time local existence of a moving boundary of the Hele-Shaw
flow with suction,
Euro. J. Appl. Math., Vol.10 (1999), pp.581-605.
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,
Asymptotic estimation for the condition numbers in BEM,
Numerische Mathematik, Vol.73 (1996), pp.209-233.
M. Kimura,
Accurate Numerical Scheme for the Flow by Curvature,
Applied Mathematics Letters, Vol.7 (1994), pp.69-73.
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.