Research
Publications
Refereed papers and proceedings
- M. Molati and H. Murakawa,
Exact solutions of nonlinear diffusion-convection-reaction equation: A Lie
symmetry analysis approach, Commun. Nonlinear Sci. Numer. Simul. , 67
(2019), pp. 253–263. DOI: 10.1016/j.cnsns.2018.06.024 link
- M. Molati and H. Murakawa, An efficient linear numerical scheme for the
Stefan problem, the porous medium equation and nonlinear cross-diffusion
systems, In K. Mikula, D. Sevcovic and J. Urban Eds. Proceedings of
Equadiff 2017 Conference, (2017), pp. 305–314. link
- H. Murakawa, An efficient linear scheme to approximate nonlinear
diffusion problems, Jpn. J. Ind. Appl. Math., 35(1) (2018), pp. 71–101.
DOI: 10.1007/s13160-017-0279-3 link
- E. Mainini, H. Murakawa, P. Piovano
and U. Stefanelli, Carbon-nanotube geometries as optimal configurations,
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal,
15(4) (2017), pp.1448–1471. DOI: 10.1137/16M1087862 link
- M. Iida, H. Monobe, H. Murakawa and H. Ninomiya, Vanishing, moving
and immovable interfaces in fast reaction limits, J. Differential Equations,
263 vol. 5 (2017), 2715–2735. DOI: 10.1016/j.jde.2017.04.009 link
- Y. Matsunaga, M. Noda, H. Murakawa, K. Hayashi, A. Nagasaka,
S. Inoue, T. Miyata, T. Miura, K. Kubo and K. Nakajima, Reelin
transiently promotes N-cadherin-dependent neuronal adhesion during
mouse cortical development, Proc. Natl. Acad. Sci. USA, 114 vol. 8 (2017),
2048–2053. DOI: 10.1073/pnas.1615215114 link
- H. Murakawa, A
linear finite volume method for nonlinear cross-diffusion systems, Numer.
Math., 136(1) (2017), 1–26. doi:10.1007/s00211-016-0832-z link
- E. Mainini, H. Murakawa,
P. Piovano and U. Stefanelli, Carbon-nanotube geometries: analytical and
numerical results, Discrete Contin. Dyn. Syst. S, 10, No.1 (2017), 141–160.
doi:10.3934/dcdss.2017008 link
- H. Murakawa and H. Togashi, Continuous models for cell-cell adhesion,
J. Theor. Biol., 372 (2015), 1–12. doi:10.1016/j.jtbi.2015.03.002 link
- H. Murakawa, Numerical solution of nonlinear cross-diffusion systems
by a linear scheme, in Proceedings for the 4th MSJ-SI Conference on
Nonlinear Dynamics in Partial Differential Equations, S. Kawashima, S.
Ei, M. Kimura and T. Mizumachi, eds., Adv. Stud. Pure Math, 64 (2015),
243–251.
- D. Hilhorst and H. Murakawa,
Singular limit analysis of a reaction-diffusion system with precipitation
and dissolution in a porous medium, Networks and Heterogeneous Media,
9(4) (2014), 669–682. doi:10.3934/nhm.2014.9.669 link
- H. Murakawa, Error estimates for discrete-time approximations of
nonlinear cross-diffusion systems, SIAM J. Numer. Anal., 52(2) (2014),
955–974. doi:10.1137/130911019 link
- H. Murakawa and H. Ninomiya, A free boundary problem in a singular
limit of a three-component reaction-diffusion system, RIMS Kokyuroku
Bessatsu, B35 (2012), 77–93.
- A. Ducrot, F. Le Foll, P. Magal, H. Murakawa, J. Pasquier and
G. Webb, An in vitro cell population dynamics model incorporating cell
size, quiescence, and contact inhibition, Math. Models Methods Appl. Sci.,
21 (2011), 871–892. DOI: 10.1142/S0218202511005404 link
- R. Eymard, D. Hilhorst, H. Murakawa and M. Olech, Numerical
approximation of a reaction-diffusion system with fast reversible reaction,
Chinese Annals of Mathematics B, 31 (2010), 631–654. link
- H. Murakawa, A linear scheme to approximate nonlinear cross-diffusion
systems, Math. Mod. Numer. Anal., 45 (2011), 1141–1161. DOI:
10.1051/m2an/2011010 link
- H. Murakawa and H. Ninomiya, Fast reaction limit of a three-component
reaction-diffusion system, DOI: 10.1016/j.jmaa.2010.12.040 J. Math. Anal.
Appl., 379 (2011), 150–170. link
- H. Murakawa, A relation between cross-diffusion
and reaction-diffusion, Discrete Contin. Dyn. Syst. S, 5 (2012), 147–158.
doi:10.3934/dcdss.2012.5.147 link
- H. Murakawa, A solution of nonlinear diffusion problems by semilinear
reaction-diffusion systems, Kybernetika, 45 (2009), 580–590. link
- H. Murakawa, Reaction-diffusion system approximation to degenerate
parabolic systems, Nonlinearity, 20 (2007), 2319–2332. link
- H. Murakawa, A regularization of a
reaction-diffusion system approximation to the two-phase Stefan problem,
Nonlinear Anal., 69 (2008), 3512–3524. link
- H. Murakawa, On reaction-diffusion system approximations to the
classical Stefan problems, Proceedings of the Czech-Japanese Seminar in
Applied Mathematics 2005, ISSN 1881-4042 (2006), 117–125.
- T. Nakaki and H. Murakawa, A numerical method to Stefan problems and
its application to the flow through porous media, European Congress on
Computational Methods in Applied Sciences and Engineering ECCOMAS
2004, 495.pdf (2004), 1–12.
- H. Murakawa and T. Nakaki, A singular limit method for the
Stefan problems, Numerical Mathematics and Advanced Applications,
Springer-Verlag, (2004), 651–657.
- H. Murakawa and T. Nakaki, A singular limit approach to moving
boundary problems and its applications, Theoretical and Applied
Mechanics Japan, 52 (2003), 255–260.
Preprints
- Hideki Murakawa, Fast reaction limit of reaction-diffusion systems,
submitted.
- Jose A. Carrillo, Hideki Murakawa, Makoto Sato, Hideru Togashi
and Olena Trush, A population dynamics model of cell-cell adhesion
incorporating population pressure and density saturation, submitted.
Supplementary Material: Movies
- O. Trush, C. Liu, X. Han, Y. Nakai, R. Takayama, H. Murakawa,
J.A. Carrillo, H. Takechi, S. Hakeda-Suzuki, T. Suzuki and M. Sato,
3D organization of columnar units by N-cadherin-dependent differential
adhesion and inter-layer interactions in the fly visual center, submitted.
Others
- G, Efp, u^
- G, Numerical analysis for nonlinear diffusion problems,
u^
- H. Murakawa, Cross-diffusion systems:
RDS approximation and Numerical analysis, u^, 1924
(2014), 21–29.
- M. Iida, H. Monobe, H. Murakawa and H. Ninomiya, The behavior of
the interfaces in the fast reaction limits of some reaction-diffusion systems
with unbalanced interactions, u^, 1892 (2014), 88–94.
- G, `gU`, u^, 1810 (2012),
189–206.
- G, gUnF_p, {w 2011 NxHG
uAuXgNg, (2011). pdf
- G, - gUp`gU, u^, 1704
(2010), 187–194.
- G, ^ゥREE, u^,
1633 (2009), 62–79.
- G, ゥREgUnp, pw
WW, (2008), 35–54.
- H. Murakawa, A reaction-diffusion system approximation to nonlinear
diffusion problems, In Ozawa, Tohru, Eds. Proceedings The 31st
Sapporo Symposium on Partial Differential Equations, Department of
Mathematics, Faculty of Science, Hokkaido University (2006).
- G, c, BK, Approximation scheme for two-phase Stefan
problems: application to the singular limit of reaction-diffusion systems,
u^, 1416 (2005), 134–147.
Presentations
Presentations (in English)
- A population dynamics model of cell-cell adhesion and its applications,
Karlstad Applied Analysis Seminar, Karlstad University, Karlstad,
Sweden, 26 Sep. 2018.
- Applications of a population dynamics model of cell-cell adhesion, Journee
d’Analyse Non Lineaire, Universite Paris-Sud 11, France, 21 Sep. 2018.
- An efficient linear scheme for nonlinear diffusion problems, The Seventh
China-Japan-Korea Joint Conference on Numerical Mathematics, Shiinoki
Cultural Complex, Kanazawa, Japan, 23 Aug. 2018.
- A continuous model of cell-cell adhesion and its applications,
Czech-Japanese Seminar in Applied Mathematics 2018, Hotel Noto
Kinpura, Noto-cho, Japan, 15 July 2018.
- A mathematical model of cell-cell adhesion and its application, The
12th AIMS Conference on Dynamical Systems, Differential Equations and
Applications, National Taiwan University, Taipei, Taiwan, 7 July 2018.
- Mathematical Modeling of Cell-cell Adhesion and its Applications, Joint
Annual Meeting of 70th JSCB and 51st JSDB, Tower Hall Funabori,
Tokyo, Japan, 7 Jun 2018. Poster.
- Fast reaction limit : classification and analysis, ReaDiNet 2017:
International Conference on Mathematical Biology, National Center for
Theoretical Sciences Mathematics in Taiwan, Taiwan, 12 Oct. 2017.
- Modeling of cell-cell adhesion and its application, Reaction-Diffusion
Systems and Mathematical Modelling in Biology, IECL Site de Nancy,
Nancy, France, 18 Sept. 2017.
- Classification and analysis of fast reaction limit problems, Ito Workshop
on Partial Differential Equations, Kyushu Univ., Fukuoka, Japan, 24 Aug.
2017.
- An efficient linear scheme for the Stefan problem, the porous medium
equation and nonlinear cross-diffusion systems, Equadiff2017, Slovak
university of technology, Bratislava, Slovakia, 28 July 2017.
- Mathematical models of cell-cell adhesion, Applied PDEs Seminar,
Imperial College London, London, UK, 14 March 2017.
- Mathematics of cell-cell adhesion: modeling and analysis, International
Workshop on Multi-Phase Flow, Waseda Univ., Tokyo, Japan, 11 Nov.
2016.
- A mathematical model of cell-cell adhesion, Reaction-Diusion Systems in
Mathematics and Biomedecine, Villa Clythia, Frejus, France, 23 Sep. 2016.
- Toward elucidation of
cell adhesion and cell sorting, Czech-Japanese-Polish Seminar in Applied
Mathematics 2016, AGH University of Science and Technology, Krakow,
Poland, 5 Sep. 2016. Poster.
- Mathematics of cell adhesion and cell sorting: experimentsC modeling and
analysis, Patterns and Waves 2016, Hokkaido univ., Hokkaido, Japan, 3
Aug. 2016. Poster.
- On a free boundary arising in a model of cell-cell adhesion, Workshop
on interface motions and free boundary problems:mathematical analysisC
numerical analysisC modellings and experiments, Isurunoie, Karuizawa,
Nagano, Japan, 10 Jul. 2016.
- Mathematics of cell-cell adhesion: experimentsC modeling and analysis,
The 11th AIMS Conference on Dynamical SystemsC Differential
Equations and Applications, Hyatt Regency, Orlando, Florida, USA, 2
Jul. 2016.
- A modified model of cell-cell adhesion, ALGORITMY 2016 Conference on
Scientific Computing, Vysoke Tatry, Podbanske, Slovakia, 17 Mar. 2016.
- Towards understanding of cell adhesion and cell sorting, Groupe de
Travail: Equations Elliptiques et Paraboliques non Lineaires, Univ.
Paris-sud, France, 15 Feb. 2016.
- Modeling and analysis of cell-cell adhesion, International conference on
mathematical modeling and applications 2015 Self-Organization Modeling
and Analysis, Meiji Univ., Tokyo, Japan, 26 Oct. 2015.
- A modified continuous model for cell-cell adhesion, 2015 Joint Meeting of
JSMB and CJK Colloquium on Mathematical Biology, Doshisya Univ.,
Kyoto, Japan, 29 Aug. 2015.
- A linear finite volume method for nonlinear cross-diffusion systems,
Mathematical Biology Conference on Cross-diffusion, chemotaxis, and
related problems, KAIST, Daejeon, Korea, 10 July 2015.
- Reaction-diffusion system approximation and fast reaction limit, 2nd
Slovak-Japan Conference on Applied Mathematics, Radzovce-Obrucna,
Cerova vrchovina, Slovakia, 14 Sept. 2014. Plenary.
- Recent topics in fast reaction limit, Workshop on Mathematical Sciences,
Wayamba University of Sri Lanka, Kuliyapitiya, Sri Lanka, 31 Aug. 2014.
- Reaction-diffusion system approximation: Theory and Applications,
Wayamba International Conference WinC 2014, Wayamba University of
Sri Lanka, Kuliyapitiya, Sri Lanka, 29 Aug. 2014
- Mathematical models of cell-cell adhesion: diffusion vs. advection, The
10th AIMS Conference on Dynamical Systems, Differential Equations and
Applications, the Universidad Autonoma de Madrid, Madrid, Spain, 8 Jul.
2014.
- Semilinear and linear approximations to nonlinear diffusion problems, The
10th AIMS Conference on Dynamical Systems, Differential Equations and
Applications, the Universidad Autonoma de Madrid, Madrid, Spain, 7 Jul.
2014.
- Cross-diffusion systems: RDS approximation and Numerical analysis,
RIMS Workshop Mathematical Analysis of Pattern Formation Arising in
Nonlinear Phenomena, Kyoto University, Japan, 31 Oct. 2013.
- Reaction-diffusion system approximation to nonlinear diffusion problems
and its application to numerical analysis, Kyushu-Euskadi 2013 Workshop
on Applied Mathematics, Fukuoka university seminar house, Japan, 12
Nov. 2013.
- Convergence rates of discrete-time schemes to approximate nonlinear
cross-diffusion systems, Czech-Japanese Seminar in Applied Mathematics
2013, Meiji University, Japan, 7 Sep. 2013.
- Error estimates for discrete-time approximations
of nonlinear cross-diffusion systems, ReaDiLab Conference Mathematical
Modelling and Analysis in the Life Sciences, Carry-le-Rouet, France, 12
Jun. 2013.
- Spatial patterns in a population model structured by cell size, quiescence
and sensing radius, Everything disperses to Miami, the role of movement
and dispersal in spatial ecology, epidemiology and environmental science,
The University of Miami, Coral Gables, Florida, USA, 14 Dec. 2012.
- Instantaneous limit of a reaction-diffusion system with a fast precipitation
and dissolution reaction, Singularities arising in Nonlinear Problems 2012,
Kansai Seminar House, 26 Nov. 2012.
- A free boundary problem with triple-junctions and a linear numerical
method for capturing the interfaces, ALGORITMY 2012 Conference on
Scientific Computing, Vysoke Tatry, Podbanske, 10 Sep. 2012.
- Approximation to nonlinear diffusion problems by semilinear
reaction-diffusion systems, Workshop of JSPS-CNR joint reserch project,
Kobe University, Japan, 3 Aug. 2012.
- On a relationship between reaction-diffusion interaction and nonlinear
diffusion, A Workshop for a Recent Development in Fluid Dynamics,
Pohang University of Science and Technology, Pohang, Korea, 19 Jul. 2012.
- Triple-junctions in a strong interaction limit of a three-component system,
The 9th AIMS Conference on Dynamical Systems, Differential Equations
and Applications, Hyatt Regency Grand Cypress, Orlando, Florida, USA,
3 Jul. 2012.
- Fast reaction limit and nonlinear diffusion, Modeling and Analysis in the
Life Sciences : A ReaDiLab Conference in Tokyo, Tokyo University, 30
Nov. 2011.
- Singular limit of a three-component reaction-diffusion system, Workshop
on Nonlinear Partial Differential Equations –China-Japan Joint Project
for Young Mathematician, East China Normal University, Shanghai,
China, 3 Nov. 2011.
- Numerical solution of nonlinear cross-diffusion systems by a linear scheme,
The 4th MSJ-SI, Mathematical Society of Japan, Seasonal Institute,
Nonlinear Dynamics in Partial Differential Equations, Kyushu University,
15 Sep. 2011.
- A free boundary problem in the limit of a fast reaction system,
Mathematical and numerical analysis for interface motion arising in
nonlinear phenomena, Kyoto University, 14 July 2011.
- Numerical simulations of nonlinear cross-diffusion systems using a
linear scheme, International Symposium on Computational Science 2011,
Kanazawa University, Kanazawa, Japan, 15 Feb. 2011.
- Reaction-diffusion system approximation to nonlinear diffusion problems
and its applications, Seminaires de Mathematiques du vivant, Universite
Bordeaux 2, France, 4 Nov. 2010.
- A linear scheme to approximate nonlinear cross-diffusion systems,
Reaction-Diffusion Systems: Experiment, Modeling and Analysis,
Universite Paris-Sud 11, France, 22 Oct. 2010.
- A numerical method for nonlinear cross-diffusion systems, Czech-Japanese
Seminar in Applied Mathematics, Faculty of Civil Engineering, branch
Telč, Czech Technical University in Prague, Telč, Czech Republic, 2 Sep.
2010.
- A relation between reaction-diffusion interaction and nonlinear diffusion,
The 8th AIMS Conference on Dynamical Systems, Differential Equations
and Applications, Dresden University of Technology, Dresden, Germany,
26 May 2010.
- A numerical method for cross-diffusion systems, Reaction-Diffusion
Systems: A ReaDiLab Seminar Day, Universite de Paris-Sud 11, France,
19 Mar. 2010.
- A solution of nonlinear diffusion problems by semilinear reaction-diffusion
systems, Spatio-Temporal Patterns from Mathematics to Biomedical
Applications, Archamps, France, 16 Mar. 2010.
- A relation between reaction-diffusion interaction and cross-diffusion,
EQUADIFF12, Masaryk University, Brno, Czech Republic, 21 Jul. 2009.
- Nonlinear diffusion problems can be approximated by semilinear
reaction-diffusion systems, PDE Approximations in Fast Reaction-Slow
Diffusion Scenarios, Lorentz center, Leiden, The Netherlands, 12 Nov.
2008. Poster and 15min talk.
- Solutions to nonlinear diffusion problems by semilinear reaction-diffusion
systems, Czech-Japanese Seminar in Applied Mathematics 2008,
Gokamura community center, Miyazaki, Japan, 1 September 2008.
- A solution of parabolic free boundary problems by semilinear
reaction-diffusion systems, Free Boundary Problems Theory and
Applications, KTH, Stockholm, Sweden, 12 Jun 2008.
- Reaction-diffusion system approximation to free boundary problems and
its application to numerical computations, International Conference on
Free Boundary Problems in Chiba 2007, Chiba University, Chiba, Japan,
29 November 2007. Poster.
- Reaction-diffusion system approximation to degenerate parabolic
equations and its application to numerical computations, Equadiff07,
Vienna University of Technology, Vienna, Austria, 8 August 2007.
- Reaction-diffusion system approximation to moving boundary problems
and its application to numerical computations, INSF2007: International
Conference on Recent Developments of Numerical Schemes for Flow
Problems, Kyushu University, Fukuoka, Japan, 27 June 2007.
- A reaction-diffusion system for nonlinear diffusion problems, Applied
Mathematics Seminar in Hiroshima 2006, Hiroshima University,
Hiroshima, Japan, November 2006.
- A reaction-diffusion system approximation to nonlinear diffusion
problems, The 31st Sapporo Symposium on Partial Differential Equations,
Hokkaido University, Hokkaido, Japan, 2 August 2006.
- On reaction-diffusion system approximations to the classical Stefan
problem, The Second Czech-Japanese Seminar in Applied Mathematics,
Kuju Training Center for the Joint Use of National Universities in Kyushu,
Oita, Japan, 16 September 2005.
- On a linear approximation scheme to the classical Stefan problem,
International Conference on Differential Equations Czecho-Slovak series,
Comenius University, Bratislava, Slovakia, 29 July 2005.
Presentations in Japanese (WEw)
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their Equilibrium States II -In honor of the retirement of Professor Yoshio
Yamada-, cw, 2018 N 9 15 .
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- Mathematical modeling of cell-cell adhesion and its applications, {p
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2017 N 3 27 .
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2017 N 2 14 .
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12 18 .
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Jw, 2016 N 12 15 .
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N 11 18 .
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Z~i[, Qw, 2016 N 6 4 .
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K), WugUnEp^[JjYv, s
w, 2004 N 10 .
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2002 NxpwW, Jw, 2002 N 12 .
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BwlZ~i[, Bw, 2002 N 11 .
Grants
- Grant-in-Aid for Scientific Research (C)(No. 17K05368) from Japan
Society for the Promotion of Science(JSPS), 2017–2020.
- Grant-in-Aid for Scientific Research (C)(No. 26400205) from Japan
Society for the Promotion of Science(JSPS), 2014–2016.
- Grant-in-Aid for Young Scientists (B)(No. 22740058) from the Ministry of
Education, Culture, Sports, Science and Technology of Japan (2010) and
from Japan Society for the Promotion of Science (2011–2012), 2010–2012.
- wh, {wpU, 2010, wQタ.
- Grant-in-Aid for Young Scientists (B)(No. 19740046) from the Ministry of
Education, Culture, Sports, Science and Technology of Japan, 2007–2009.
- Grant-in-Aid for JSPS Fellows (No. 17.5994) from the Ministry of
Education, Culture, Sports, Science and Technology of Japan, 2005.
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