1. |
H. Murakawa, An efficient linear scheme to approximate nonlinear diffusion problems, *Jpn. J. Ind. Appl. Math.*, 35, 1, 71-101, 2018.03. |

2. |
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, 1448-1471, 2017.10. |

3. |
M. Iida, H. Monobe, H. Murakawa and H. Ninomiya, Immovable, moving and vanishing interfaces in fast reaction limit, *J. Differential Equations*, 263, 5, 2715-2735, 2017.09. |

4. |
H. Murakawa, A linear finite volume method for nonlinear cross-diffusion systems, *Numer. Math.*, 136, 1, 1-26, 2017.05. |

5. |
E. Mainini, H. Murakawa, P. Piovano and U. Stefanelli, Carbon-nanotube geometries: analytical and numerical results, *Discrete Contin. Dyn. Syst. S*, 10, 141-160, 2017.02. |

6. |
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, 8, 2048-2053, 2017.02, Reelin is an essential glycoprotein for the establishment of the highly organized six-layered structure of neurons of the mammalian neocortex. Although the role of Reelin in the control of neuronal migration has been extensively studied at the molecular level, the mechanisms underlying Reelin-dependent neuronal layer organization are not yet fully understood. In this study, we directly showed that Reelin promotes adhesion among dissociated neocortical neurons in culture. The Reelin-mediated neuronal aggregation occurs in an N-cadherin–dependent manner, both in vivo and in vitro. Unexpectedly, however, in a rotation culture of dissociated neocortical cells that gradually reaggregated over time, we found that it was the neural progenitor cells [radial glial cells (RGCs)], rather than the neurons, that tended to form clusters in the presence of Reelin. Mathematical modeling suggested that this clustering of RGCs could be recapitulated if the Reelin-dependent promotion of neuronal adhesion were to occur only transiently. Thus, we directly measured the adhesive force between neurons and N-cadherin by atomic force microscopy, and found that Reelin indeed enhanced the adhesiveness of neurons to N-cadherin; this enhanced adhesiveness began to be observed at 30 min after Reelin stimulation, but declined by 3 h. These results suggest that Reelin transiently (and not persistently) promotes N-cadherin–mediated neuronal aggregation. When N-cadherin and stabilized β-catenin were overexpressed in the migrating neurons, the transfected neurons were abnormally distributed in the superficial region of the neocortex, suggesting that appropriate regulation of N-cadherin–mediated adhesion is important for correct positioning of the neurons during neocortical development.. |

7. |
H. Murakawa and H. Togashi, Continuous models for cell-cell adhesion, *J. Theor. Biol.*, 2015.06, Cell adhesionisthebindingofacelltoanothercellortoanextracellularmatrixcomponent.Thisprocess is essentialinorganformationduringembryonicdevelopmentandinmaintainingmulticellular structure. Armstrongetal.(2006)[J.Theor.Biol.243,pp.98–113]proposedanonlocaladvection– diffusion systemasapossiblecontinuousmathematicalmodelforcell–cell adhesion.Althoughthe systemisattractiveandchallenging,itgivesbiologicallyunrealisticnumericalsolutionsunder certain situations.Weidentifytheproblemsandchangeunderlyingideaofcellmovementfrom “cells moverandomly” to “cells movefromhightolowpressureregions”. Thenweprovideamodified continuous modelforcell–cell adhesion.Numericalexperimentsillustratethatthemodified modelis able toreplicatenotonlySteinberg'scellsortingexperimentsbutalsosomephenomenawhichcannot be capturedatallbyArmstrong–Painter–Sherratt model.. |

8. |
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*, 2014.12. |

9. |
H. Murakawa, Error estimates for discrete-time approximations of nonlinear cross-diffusion systems, *SIAM J. Numer. Anal.*, 2014.04. |

10. |
H. Murakawa, A relation between cross-diffusion and reaction-diffusion, *Discrete Contin. Dyn. Syst. S*, 5, 147-158, 2012.02. |

11. |
H. Murakawa, A linear scheme to approximate nonlinear cross-diffusionsystems, *Math. Mod. Numer. Anal.*, 45, 1141-1161, 2011.11. |

12. |
H. Murakawa and H. Ninomiya, Fast reaction limit of a three-componentreaction-diffusion system, *J. Math. Anal. Appl.*, 379, 150-170, 2011.07. |

13. |
A. Ducrot, F. Le Foll, P. Magal, H. Murakawa, J. Pasquier and G. Webb, An in vitro cell population dynamics model incorporating cellsize, quiescence, and contact inhibition, *Math. Models Methods Appl. Sci.*, 21, 871-892, 2011.04. |

14. |
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, 631-654, 2010.09. |