IIDA Masato



Engineering educational research section Science Center for Engineering Education



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Degree 【 display / non-display

  • 博士(理学) ( 1995.3   大阪大学 )

  • 理学修士 ( 1989.3   大阪大学 )

Research Areas 【 display / non-display

  • Natural Science / Mathematical analysis


Papers 【 display / non-display


    Iida M., Izuhara H., Kon R.

    Discrete and Continuous Dynamical Systems - Series B   28 ( 12 )   6159 - 6178   2023.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Discrete and Continuous Dynamical Systems - Series B  

    Cross-diffusion may be an important driving force of pattern formation in population models. Recently, a relation between cross-diffusion and reaction-diffusion systems has been revealed from the mathematical modeling point of view. In this paper, we derive a predator–prey model with cross-diffusion from a simple reaction-diffusion system with two behavioral states in the predator population and examine whether cross-diffusion can induce spatial patterns in predator–prey models. We assume that the predators have identical behavioral characteristics except for their mobility and searching activity for preys: we consider two states, namely less mobile predators searching for preys more actively than mobile predators. Our analysis shows that cross-diffusion derived in this situation can induce spatial patterns if the prey-density-dependent conversion rate from less mobile state to mobile one increases more rapidly than that from mobile to less mobile at high prey density.

    DOI: 10.3934/dcdsb.2023098


  • Vanishing, moving and immovable interfaces in fast reaction limits Reviewed

    M. Iida, H. Monobe, H. Murakawa, H. Ninomiya

    Journal of Differential Equations   263 ( 5 )   2715 - 2735   2017.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    We consider a type of singular limit problem called the fast reaction limit. The problem of the fast reaction limit involves studying the behaviour of solutions of reaction–diffusion systems when the reaction speeds are very fast. Fast reaction limits of two-component systems have been studied in recent decades. In most of these systems, the fast reaction terms of each component are represented by the same function. Fast reaction limits of systems with different fast reaction terms are still far from being well understood. In this paper, we focus on a reaction–diffusion system for which the reaction terms consist of monomial functions of various powers. The behaviour of interfaces arising in the fast reaction limit of this system is studied. Depending on the powers, three types of behaviour are observed: (i) the initial interface vanishes instantaneously, (ii) the interface propagates at a finite speed, and (iii) the interface does not move.

    DOI: 10.1016/j.jde.2017.04.009

  • The behavior of the interfaces in the fast reaction limits of some reaction-diffusion systems with unbalanced interactions Invited

    Masato Iida, Harunori Monobe, Hideki Murakawa and Hirokazu Ninomiya

    数理解析研究所講究録   ( 1892 )   88 - 94   2014.4

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    Language:English   Publishing type:Research paper (other academic)  

  • Different degrees of reaction rates can block interfacial dynamics in reaction-diffusion systems

    Masato Iida

    Proceedings of Seminar on Partial Differential Equations in Osaka 2012 ―in honor of Professor Hiroki Tanabe's 80th birthday―   39 - 43   2013.3

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    Language:English   Publishing type:Research paper (international conference proceedings)  

    DOI: http://ir.library.osaka-u.ac.jp/dspace/handle/11094/24563

  • Stacked fronts for cooperative systems with equal diffusion coefficients(共著) Reviewed

    Masato Iida, Roger Lui and Hirokazu Ninomiya

    SIAM Journal on Mathematical Analysis   43 ( 3 )   1369 - 1389   2011.6

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    Language:English   Publishing type:Research paper (scientific journal)  

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MISC 【 display / non-display

  • A review on reaction-diffusion approximation Invited Reviewed

    M. Iida, H. Ninomiya, H. Yamamoto

    Journal of Elliptic and Parabolic Equations   4 ( 2 )   565 - 600   2018.12

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    Language:English   Publishing type:Article, review, commentary, editorial, etc. (scientific journal)   Publisher:Springer International Publishing  

    Recently reaction-diffusion approximation has been intensively studied. This paper reviews the studies in reaction-diffusion approximation. This paper explains reaction-diffusion approximation of the Stefan problem, nonlinear diffusion, nonlocal dispersal and wave equations. Moreover, some instabilities of equations mentioned above will be explained by the Turing instability through reaction-diffusion approximations.

    DOI: 10.1007/s41808-018-0029-y

  • Reaction-diffusion approximation and its related topics Invited Reviewed

    Masato Iida, Hirokazu Ninomiya

    Sugaku   66 ( 3 )   225 - 248   2014.7

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    Language:Japanese   Publishing type:Research paper, summary (national, other academic conference)   Publisher:The Mathematical Society of Japan, Iwanami Shoten  

  • Interfacial Dynamics as Singular Limits of Some PDEs ― Method of Matched Asymptotic Expansion ― Invited


    数理解析研究所講究録   1123   1 - 19   2000.1

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    Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (other)   Publisher:京都大学数理解析研究所  

Presentations 【 display / non-display

  • 反応拡散系の急速反応極限によって見えるもの


    2009日本数学会秋季総合分科会函数方程式論分科会  (大阪大学豊中キャンパス)  日本数学会

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    Event date: 2009.9.24 - 2009.9.27

    Language:Japanese   Presentation type:Oral presentation (invited, special)  


  • 反応拡散近似とは―基本的アイデアと可能性―


    応用数学勉強会2015@芝浦工大  (芝浦工業大学大宮キャンパス)  石渡哲哉(芝浦工業大学),高坂良史(神戸大学)

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    Event date: 2015.10.29 - 2015.10.31

    Language:Japanese   Presentation type:Oral presentation (keynote)  


  • 接合漸近展開法による界面の運動方程式の導出


    短期共同研究「数理物理に現れる非線形発展方程式の特異点の解析的研究」  (京都大学数理解析研究所)  小川卓克

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    Event date: 1998.5.25 - 1998.5.29

    Language:Japanese   Presentation type:Oral presentation (keynote)  


  • 交差拡散系に帰着される捕食者・被食者モデル ー 二つの捕獲様式を切り替える捕食者

    飯田 雅人、出原浩史、今隆助

    2023秋の偏微分方程式セミナー  2023.9.5 

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    Event date: 2023.9.4 - 2023.9.5

    Language:Japanese   Presentation type:Oral presentation (general)  

  • Reconsideration of fast reaction limits from the viewpoints of matched asymptotic expansions Invited

    Masato Iida

    T. Kawakami, Y. Morita, Y. Kabeya, T. Mori

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    Event date: 2019.3.22 - 2019.3.23

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:Seta Campus 1-534, Ryukoku University  

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Grant-in-Aid for Scientific Research 【 display / non-display

  • 反応拡散系とその特異極限形に現れるパターンダイナミクスの数理解析

    Grant number:20H01816  2020.04 - 2024.03

    独立行政法人日本学術振興会  科学研究費補助金  基盤研究(B)

    飯田 雅人

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  • 漸近解構築に基づく反応拡散系の解の形と動きの解明

    2015.04 - 2019.03

    科学研究費補助金  基盤研究(C)

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    Authorship:Principal investigator 


  • 反応拡散系および自由境界問題の解のパターンダイナミクスの解明

    2014.04 - 2018.03

    科学研究費補助金  基盤研究(B)

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  • 反応拡散系の漸近解構築への理論的アプローチ

    2012.04 - 2015.03

    科学研究費補助金  基盤研究(C)

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    Authorship:Principal investigator 


Other research activities 【 display / non-display

  • 研究集会「数学と現象:Mathematics and Phenomena in Miyazaki 2023」の世話人


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  • 研究集会「数学と現象:Mathematics and Phenomena in Miyazaki 2019」の世話人


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  • 研究集会「数学と現象:Mathematics and Phenomena in Miyazaki 2018」の世話人


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  • 研究集会「数学と現象:Mathematics and Phenomena in Miyazaki 2017」の世話人


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  • 研究集会「数学と現象:Mathematics and Phenomena in Miyazaki 2016」の世話人


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