Doctor of Science, Hokkaido University

Localized patterns

Nonlocal reaction-diffusion equations

Nonlocal effect

Reaction-diffusion equations

Natural Science, Mathematical analysis

Natural Science, Applied mathematics and statistics

Bachelor's degree program, School of Science

Master's degree program, Graduate School of Science

Doctoral (PhD) degree program, Graduate School of Science

May 2020, 北海道大学大学院理学院, 優秀研究奨励賞

Reaction, diffusion, and nonlocal interaction in high-dimensional space
Hiroshi Ishii; Yoshitaro Tanaka
Journal of Mathematical Biology, 92, 5, Springer Science and Business Media LLC, 09 Apr. 2026, [Peer-reviewed]
English, Scientific journal, 47575048;50477209;42269740

Spot solutions to a neural field equation on oblate spheroids
Hiroshi Ishii; Riku Watanabe
Communications in Nonlinear Science and Numerical Simulation, 152, 109172, 109172, Elsevier BV, Jan. 2026, [Peer-reviewed], [Lead author, Corresponding author], [International Magazine]
English, Scientific journal, 47575048;42269740

A mathematical model of human oesophageal motility function
Takashi Miura; Hiroshi Ishii; Yoshitaka Hata; Hisako Takigawa-Imamura; Kei Sugihara; Shin-Ichiro Ei; Xiaopeng Bai; Eikichi Ihara; Yoshihiro Ogawa
Royal Society Open Science, 12, 8, The Royal Society, 20 Aug. 2025, [Peer-reviewed], [International Magazine]
English, Scientific journal, Recent advances in various observation methods revealed several unique characteristics of oesophageal peristalsis and its disorders. However, a framework for understanding the oesophageal motility pattern is lacking. Here, we propose a simple mathematical model of the human oesophageal motility function. The model comprises central nervous system signals, enteric nervous system neurons (interneurons and motoneurons) and oesophageal smooth muscles. The neural function implements excitable dynamics at the oesophageal body and toggle-switch dynamics at the lower oesophageal sphincter. The local signal transmission in enteric nervous system and ‘the law of the intestine’ were also incorporated. The model behaviours can be understood using mathematical analysis, and we could reproduce the physiological dynamics of the normal oesophagus—deglutitive inhibition, unidirectional pulse transmission, restoration of lower oesophageal sphincter constriction and dilatation of the anal side of the pulse. In addition, we could reproduce various pathological motility patterns described in the Chicago classification by the combinations of parameter changes, which may provide insights into the possible pathogenesis of these disorders., 36726069

Propagating front solutions in a time-fractional Fisher-KPP equation
Hiroshi Ishii
Discrete and Continuous Dynamical Systems - B, 30, 7, 2460, 2482, American Institute of Mathematical Sciences (AIMS), 2025, [Peer-reviewed], [Lead author, Last author, Corresponding author], [International Magazine]
English, Scientific journal, 47575048;42269740

Asymptotic profiles of zero points of solutions to the heat equation
Hiroshi Ishii
Proceedings of the American Mathematical Society, 152, 10, 4451, 4461, American Mathematical Society (AMS), 07 Aug. 2024, [Peer-reviewed], [Lead author, Last author, Corresponding author], [International Magazine]
English, Scientific journal,

In this paper, we consider the asymptotic profiles of zero points for the spatial variable of the solutions to the heat equation. By giving suitable conditions for the initial data, we prove the existence of zero points by extending the high-order asymptotic expansion theory for the heat equation. This reveals a previously unknown asymptotic profile of zero points diverging at . In a one-dimensional spatial case, we show the zero point’s second and third-order asymptotic profiles in a general situation. We also analyze a zero level set in high-dimensional spaces and obtain results that extend the results for the one-dimensional spatial case.

, 42269740;36726069

The motion of weakly interacting localized patterns for reaction-diffusion systems with nonlocal effect
Ei, S.-I.; Ishii, H.
Discrete and Continuous Dynamical Systems - Series B, 26, 1, 173, 190, American Institute of Mathematical Sciences (AIMS), 2021, [Peer-reviewed], [International Magazine]
Scientific journal

Effective nonlocal kernels on reaction–diffusion networks
Shin-Ichiro Ei; Hiroshi Ishii; Shigeru Kondo; Takashi Miura; Yoshitaro Tanaka
Journal of Theoretical Biology, 509, 110496, 110496, Elsevier BV, Jan. 2021, [Peer-reviewed], [International Magazine]
English, Scientific journal, A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called "effective equation" including the reduced integral kernel (called "effective kernel") in the convolution type. As one typical example, the Mexican hat shaped kernel is theoretically derived from two component activator-inhibitor systems. It is also shown that a three component system with quite different appearance from activator-inhibitor systems is reduced to an effective equation with the Mexican hat shaped kernel. It means that the two different systems have essentially the same effective equations and that they exhibit essentially the same spatial and temporal patterns. Thus, we can identify two different systems with the understanding in unified concept through the reduced effective kernels. Other two applications of this method are also given: Applications to pigment patterns on skins (two factors network with long range interaction) and waves of differentiation (called proneural waves) in visual systems on brains (four factors network with long range interaction). In the applications, we observe the reproduction of the same spatial and temporal patterns as those appearing in pre-existing models through the numerical simulations of the effective equations.

Noise-induced scaling in skull suture interdigitation
Naroda, Y.; Endo, Y.; Yoshimura, K.; Ishii, H.; Ei, S.-I.; Miura, T.
PLoS ONE, 15, 12 December, e0235802, e0235802, Public Library of Science (PLoS), 17 Dec. 2020, [Peer-reviewed], [International Magazine]
Scientific journal

A continuation method for spatially discretized models with nonlocal interactions conserving size and shape of cells and lattices
Ei, S.-I.; Ishii, H.; Sato, M.; Tanaka, Y.; Wang, M.; Yasugi, T.
Journal of Mathematical Biology, 81, 4-5, 981, 1028, Springer Science and Business Media LLC, Nov. 2020, [Peer-reviewed], [International Magazine]
Scientific journal

Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel
Ei, S.-I.; Guo, J.-S.; Ishii, H.; Wu, C.-C.
Journal of Mathematical Analysis and Applications, 487, 2, 124007, 124007, Elsevier BV, Jul. 2020, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
Scientific journal

Transitions to slow or fast diffusions provide a general property for in-phase or anti-phase polarity in a cell
Seirin-Lee, S.; Sukekawa, T.; Nakahara, T.; Ishii, H.; Ei, S.-I.
Journal of Mathematical Biology, 80, 6, 1885, 1917, Springer Science and Business Media LLC, May 2020, [Peer-reviewed], [International Magazine]
Scientific journal

Morphology-Driven Inference of Patient-Specific Pathophysiological States Enables Precision Treatment in Chronic Spontaneous Urticaria
Sungrim Seirin-Lee; Takahiro hiraga; Hiroshi Ishii; Ryo Saito; Daiki Matsubara; Shunsuke Takahagi; Michihiro Hide, 17 Jan. 2026
Skin diseases manifest as visually observable eruption patterns, making image-based assessment a central component of dermatological diagnosis. While recent artificial intelligence (AI)-based approaches have achieved remarkable progress in classifying skin diseases from images, their utility remains largely limited to pattern recognition tasks, such as disease identification or severity grading. Crucially, most existing AI frameworks operate as black-box classifiers and do not provide interpretable links between eruption morphology and the underlying in vivo pathophysiological states, thereby offering limited support for personalized treatment decisions. To date, no practical framework has been established to systematically translate eruption morphology into mechanistic insights or treatment-relevant predictions for inflammatory skin diseases such as chronic urticaria.Here, we propose a novel integrative framework that infers patient-specific pathophysiological states directly from skin eruption morphology. Our approach unifies mechanistic mathematical modeling with data science that encompasses machine learning and topological data analysis, together with in vitro experiments and clinical data into a single coherent system. By constructing a mathematical model that explicitly links disease pathophysiology to eruption morphology, we develop a computational parameter inference tool, the System for Skin Eruption Morphology-based Parameter Inference (SEMPi), that estimates patient-specific physiological parameters directly from real-world skin eruption images. Importantly, these inferred parameters are interpretable in terms of underlying biological processes, enabling direct insight into patient-specific disease states rather than mere image-level classification. Furthermore, by incorporating drug interactions into the mathematical model, our framework enables treatment-response prediction and optimization of individualized therapeutic strategies across multiple drugs. This study introduces a paradigm shift from morphology-based classification toward morphology-driven interpretation of patient physiology, providing a foundation for predictive diagnosis and precision treatment in inflammatory skin diseases., openRxiv

Relationship between haptotaxis and chemotaxis in cell dynamics
Hiroshi Ishii; Hideki Murakawa; Yoshitaro Tanaka, 01 Mar. 2025
The phenomenon where cells with elongated protrusions, such as neurons, communicate by contacting other cells and arrange themselves appropriately is termed cell sorting through haptotaxis. This phenomenon is described by partial differential equations involving nonlocal advection. In contrast, cell phenomena where cells communicate with other cells via chemical substances and arrange themselves appropriately are termed cell sorting through chemotaxis, typically modeled by chemotactic systems such as the Keller--Segel model. Although there are clear differences between haptotaxis and chemotaxis, similar behaviors are often observed. In this study, we investigate the relationship between haptotaxis and chemotaxis in cell sorting phenomena. Specifically, we analyze the connections between a nonlocal aggregation model for haptotaxis and a Keller--Segel type chemotaxis system. By demonstrating convergence under specific kernel approximations, we show how these distinct mechanisms can lead to comparable dynamic behaviors. In particular, we establish that the gradient of a given kernel can be approximated by linear combinations of gradients of fundamental solutions, which also provides a mathematical contribution of independent interest. This study provides a mathematical framework for understanding the interplay between haptotaxis and chemotaxis in cell sorting phenomena., 50477209;42269740;47575048

On the approximation of spatial convolutions by PDE systems
Hiroshi Ishii; Yoshitaro Tanaka, arXiv:2412.19539, Dec. 2024, [Corresponding author]
This paper considers the approximation of spatial convolution with a given radial integral kernel. Previous studies have demonstrated that approximating spatial convolution using a system of partial differential equations (PDEs) can eliminate the analytical difficulties arising from integral formulations in one-dimensional space. In this paper, we establish a PDE system approximation for spatial convolutions in higher spatial dimensions. We derive an appropriate approximation function for given arbitrary radial integral kernels as a linear sum of Green functions. In establishing the validity of this methodology, we introduce an appropriate integral transformation to show the completeness of the basis constructed by the Green functions. This framework enables the approximation of nonlocal convolution-type operators with arbitrary radial integral kernels using linear sums of PDE solutions. Finally, we present numerical examples that illustrate the effectiveness of our proposed method., English, Technical report, 47575048;42269740

Correction to: A continuation method for spatially discretized models with nonlocal interactions conserving size and shape of cells and lattices
Shin-Ichiro Ei; Hiroshi Ishii; Makoto Sato; Yoshitaro Tanaka; Miaoxing Wang; Tetsuo Yasugi, Journal of Mathematical Biology, 82, 6, 08 May 2021
Springer Science and Business Media LLC

非局所反応拡散方程式における定常フロント解同士の相互作用
石井宙志; 栄伸一郎, 第17回数学総合若手研究集会-北海道大学数学講究録-,, 180, 471, 478, Mar. 2021
Japanese

Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel
Hiroshi Ishii, Proceedings of 45th Sapporo Symposium on Partial Differential Equations-北海道大学数学講究録-, 71, 79, Aug. 2020, [Invited]

符号変化する積分核を有する時間発展方程式における進行波解の存在について
栄伸一郎; Jong-Shenq Guo; 石井宙志; Chin-Chin Wu, 第16回数学総合若手研究集会-北海道大学数学講究録-, 北海道大学, 178, 473, 480, Mar. 2020
Japanese

符号変化が伴う非局所分散項を持つFisher-KPP方程式における進行波解の存在について
石井宙志, 第41回若手発展方程式セミナー報告集, 67, 74, Feb. 2020

球面上における分化の波の数値計算
石井宙志; 栄伸一郎; 佐藤純; 八杉徹雄, 第15回数学総合若手研究集会-北海道大学数学講究録-, 176, 631, 638, Mar. 2019
Japanese

〔主要な業績〕グラフ上のパルス伝播問題 II
石井宙志
応用数学交流研究会2026, 14 Feb. 2026, Japanese, Invited oral presentation
13 Feb. 2026 - 15 Feb. 2026, 50477209, [Invited]

〔主要な業績〕Propagating front solutions in a time-fractional Fisher-KPP type equation
Hiroshi ISHII
第7回城西大学数理応用セミナーWS 伝播現象の数理, 09 Feb. 2026, Japanese, Invited oral presentation
09 Feb. 2026 - 10 Feb. 2026, 42269740;47575048, [Invited]

〔主要な業績〕高次元空間における非局所相互作用の反応拡散近似
石井宙志; 田中吉太郎
2025年度応用数学合同研究集会, 20 Dec. 2025, Japanese, Oral presentation
18 Dec. 2025 - 20 Dec. 2025, 47575048;50477209;42269740

〔Major achievements〕Propagating front solutions in a time-fractional Fisher-KPP equation
Hiroshi ISHII
ReaDiNet 2025: International Conference on Recent Topics in Reaction-Diffusion Systems and Their Applications, 24 Oct. 2025, English, Invited oral presentation
20 Oct. 2025 - 24 Oct. 2025, 47575048;42269740, [Invited]

〔主要な業績〕球面および楕円体上における神経場方程式のスポット解について
石井宙志
第3回諏訪偏微分方程式研究集会, 08 Sep. 2025, Japanese, Invited oral presentation
08 Sep. 2025 - 09 Sep. 2025, 47575048;42269740, [Invited]

グラフ上のパルス伝播問題
石井宙志
応用数学交流研究会2025 夏, 08 Aug. 2025, Japanese, Invited oral presentation
06 Aug. 2025 - 09 Aug. 2025, 50477209, [Invited]

非局所反応拡散方程式のパターン形成問題
石井宙志
応用数学交流研究会2025 冬, 06 Feb. 2025, Japanese, Invited oral presentation
05 Feb. 2025 - 08 Feb. 2025, 47575048;42269740, [Invited]

Propagating front solutions to Fisher-KPP equation with a time-fractional derivative
Hiroshi ISHII
The 14th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 18 Dec. 2024, English, Invited oral presentation
16 Dec. 2024 - 20 Dec. 2024, 47575048;42269740, [Invited]

時間非整数階微分を持つFisher-KPP型方程式の解の伝播について
石井宙志
Okayama Workshop on PDEs, 26 Oct. 2024, Japanese, Invited oral presentation
26 Oct. 2024 - 26 Oct. 2024, 47575048;42269740, [Invited]

時間非整数階微分を持つFisher-KPP型方程式の解の伝播について
石井宙志
京都駅前セミナー, 11 Oct. 2024, Japanese, Invited oral presentation
11 Oct. 2024 - 11 Oct. 2024, 47575048;42269740, [Invited]

非整数階時間微分を持つFisher-KPP型方程式の進行波解について
石井宙志
日本数学会 2024年度秋季総合分科会, 06 Sep. 2024, Japanese
03 Sep. 2024 - 06 Sep. 2024, 47575048;42269740

時間非整数階微分を持つFisher-KPP型方程式の解の伝播について
石井宙志
第１回北見数理科学研究会, 27 Aug. 2024, Japanese
26 Aug. 2024 - 27 Aug. 2024, 47575048;42269740, [Invited]

非局所反応拡散方程式の解の時空間ダイナミクスにおける積分核形状の影響
石井宙志
北海道大学数学教室・談話会, 04 Jul. 2024, Japanese, Invited oral presentation
04 Jul. 2024 - 04 Jul. 2024, 42269740;47575048, [Invited]

Pattern Formation in Mathematical Models Including Neuronal Interaction Effects
Hiroshi ISHII
Digital Brain Seminar, 22 Apr. 2024, English, Invited oral presentation
22 Apr. 2024 - 22 Apr. 2024, 42269740;47575048, [Invited]

On the propagation of solutions to Fisher-KPP type equation with time-fractional derivative
Hiroshi ISHII
Hokudai-NYCU Joint Workshop on Applied Mathematics, 12 Apr. 2024, English, Invited oral presentation
11 Apr. 2024 - 12 Apr. 2024, 42269740;47575048, [Invited]

時間非整数階微分を持つFisher-KPP型方程式の解の挙動について
石井宙志
第13回室蘭非線形解析研究会, 21 Jan. 2024, Japanese, Invited oral presentation
20 Jan. 2024 - 21 Jan. 2024, 42269740, [Invited]

非局所項を持つ反応拡散モデルのパターン形成問題
石井宙志
令和5年度電子研交流会, 05 Jan. 2024, Japanese
05 Jan. 2024 - 05 Jan. 2024

Effect of integral kernel shape on interface dynamics in a nonlocal bistable equation
Hiroshi ISHII
MATHEMATICAL ASPECTS OF CONTINUUM MECHANICS 2023, 11 Dec. 2023, English, Invited oral presentation
11 Dec. 2023 - 12 Dec. 2023, 42269740, [Invited]

Propagating front solutions in time-fractional Fisher-KPP equations
Hiroshi Ishii
Geometric aspect of partial differential equations, 05 Dec. 2023, English, Invited oral presentation
04 Dec. 2023 - 06 Dec. 2023, [Invited]

非局所反応拡散方程式に現れる界面の運動について
石井宙志
第3回はこだて現象数理研究集会, 16 Nov. 2023, Japanese, Invited oral presentation
16 Nov. 2023 - 17 Nov. 2023, 42269740, [Invited]

Motion of phase-separated patterns in nonlocal reaction-diffusion equations
Hiroshi ISHII
RIMS Conference "Multidisciplinary Research on Nonlinear Phenomena: Modeling, Analysis and Applications", 09 Nov. 2023, English, Invited oral presentation
08 Nov. 2023 - 10 Nov. 2023, 42269740, [Invited]

Propagation speeds of solutions in time-fractional Fisher-KPP equarions
Hiroshi ISHII
ReaDiNet: International Conference on Recent Developments of Theory and Methods in Mathematical Biology, 24 Oct. 2023, English, Poster presentation
23 Oct. 2023 - 27 Oct. 2023, 42269740

Dynamics of localization patterns in some nonlocal evolution equations
Hiroshi ISHII
ICIAM2023, 21 Aug. 2023, English, Oral presentation
20 Aug. 2023 - 25 Aug. 2023, 42269740

Effects of a nonlocal term in pattern formation problems
Hiroshi ISHII
Biwako workshop on Mathematical Biology, 17 Aug. 2023, English, Invited oral presentation
16 Aug. 2023 - 19 Aug. 2023, 42269740, [Invited]

非局所反応拡散方程式における局在パターンの積分核形状に依存した挙動について
石井宙志
反応拡散系パターンダイナミクスの新展開, 24 Jun. 2023, Japanese, Invited oral presentation
22 Jun. 2023 - 24 Jun. 2023, 42269740, [Invited]

Spatio-Temporal Patterns in Nonlocal Reaction-Diffusion Equations Dependent on the Integral Kernel Shape
石井宙志
京都大学応用数学セミナー, 20 Jun. 2023, Japanese, Invited oral presentation
42269740, [Invited]

Traveling waves to a nonlocal scalar equation with sign-changing kernel
Hiroshi ISHII
The 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications "SS08 Propagation Phenomena in Reaction-Diffusion Systems", 01 Jun. 2023, English, Invited oral presentation
31 May 2023 - 04 Jun. 2023, 42269740, [Invited]

Dynamics of localized patterns in nonlocal reaction-diffusion equations depending on the integral kernel shape
Hiroshi ISHII
NCTS Webinar on Nonlinear Evolutionary Dynamics, 12 Apr. 2023, English, Invited oral presentation
12 Apr. 2023 - 12 Apr. 2023, 42269740, [Invited]

十分弱い非局所効果を持つ反応拡散方程式における積分核形状に依存したパターンダイナミクス
石井宙志
日本数学会2023年度年会, 18 Mar. 2023, Japanese, Oral presentation
15 Mar. 2023 - 18 Mar. 2023, 36726069

ヒト食道運動の数理モデルと食道運動異常症
石井宙志
数学と諸分野の連携に向けた若手数学者交流会（第4回）2023, 13 Mar. 2023, Japanese, Poster presentation
13 Mar. 2023 - 14 Mar. 2023, 36726069

Dynamics of localized patterns in nonlocal evolution equations
Hiroshi ISHII
Methods and Applications in Mathematical Life Sciences, 17 Feb. 2023, English, Oral presentation

Dynamics of localized patterns in reaction-diffusion equations with nonlocal effect
Hiroshi ISHII
Kyoto-Vienna biomath workshop, 02 Dec. 2022, English, Invited oral presentation
01 Dec. 2022 - 01 Dec. 2022, [Invited]

食道運動の数理モデルと食道運動異常症
石井 宙志; 三浦 岳; 畑 佳孝; 今村 寿子; 栄 伸一郎; 伊原 栄吉; 小川 佳宏
日本応用数理学会2022年度年会, 10 Sep. 2022, Japanese
36726069, [Invited]

非局所反応拡散方程式の積分核形状に依存したパターンダイナミクスについて
石井宙志
日本応用数理学会2022年度年会, 09 Sep. 2022, Japanese, Invited oral presentation
36726069, [Invited]

Spatio-temporal dynamics of solutions for nonlocal reaction-diffusion equations depending on the integral kernel shape
Hiroshi ISHII
日本数理生物学会2020年度年会, 06 Sep. 2022
06 Sep. 2022 - 08 Sep. 2022, 36726069, [Invited]

Spatio-temporal dynamics of solutions to nonlocal reaction-diffusion equations depending on the shape of integral kernel
Hiroshi ISHII
京都駅前セミナー, 08 Jul. 2022
[Invited]

Asymptotic profiles of zero points of solutions to nonlocal diffusion equations
Hiroshi ISHII
The 23rd northeastern symposium on mathematical analysis, Feb. 2022, English, Invited oral presentation
[Invited]

パターン形成問題に対する積分核を用いた表現方法と分化の波への応用
石井宙志
細胞ダイバーシティーの統合的解明と制御 第4回若手ワークショップ, Jan. 2022, Poster presentation

拡散現象を記述する偏微分方程式における解の零点の漸近挙動について
石井宙志
数理解析若手交流会, Nov. 2021, Invited oral presentation
[Invited]

非局所反応拡散方程式におけるフロント解同士の相互作用について
石井宙志; 栄伸一郎
日本数学会2021年度年会, Mar. 2021, Oral presentation

非局所反応拡散方程式における定常フロント解同士の相互作用
石井宙志
第17回数学総合若手研究集会, Mar. 2021, Oral presentation

Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel
石井宙志
第14回若手のための偏微分方程式と数学解析, Feb. 2021, Invited oral presentation
[Invited]

非局所反応拡散方程式における局在パターン同士の弱い相互作用
石井宙志
北陸応用数理研究会2021, Feb. 2021, Invited oral presentation
[Invited]

非局所反応拡散方程式におけるフロント解の相互作用について
石井宙志; 栄伸一郎
2020年度応用数学合同研究集会, Dec. 2020, Oral presentation

非局所反応拡散方程式におけるフロント解の相互作用
石井宙志
応用数学フレッシュマンセミナー2020, Dec. 2020, Invited oral presentation
[Invited]

Motion of interacting front solutions for nonlocal reaction diffusion equations
Hiroshi ISHII
ReaDiNet 2020: An online conference on mathematical biology, Oct. 2020, English, Invited oral presentation
[Invited]

非局所反応拡散方程式におけるフロント解同士の相互作用について
石井宙志; 栄伸一郎
日本応用数理学会2020年度年会, Sep. 2020, Oral presentation

非局所反応拡散方程式におけるフロント解同士の相互作用
石井宙志
第14回応用数理研究会, Sep. 2020, Oral presentation

Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel
石井宙志
45th Sapporo Symposium on Partial Differential Equations, Aug. 2020, Invited oral presentation
[Invited]

食道運動異常症と数理モデル
三浦岳; 石井宙志
反応拡散系と実験の融合3, Feb. 2020, Invited oral presentation
[Invited]

The motion of weak interacting localized patterns with nonlocal interactions
Hiroshi ISHII; Shin-Ichiro EI
The 21st northeastern symposium on mathematical analysis, Feb. 2020, English, Poster presentation

符号変化を伴う積分核を持つ時間発展方程式における進行波解の存在
栄伸一郎; Jong-Shenq Guo; 石井宙志; Chin-Chin Wu
2019年度応用数学合同研究集会, Dec. 2019, Oral presentation

反応拡散ネットワークに基づいた本質的積分核の導出と分化の波への応用
石井宙志
定量生物学キャラバン 北海道キャラバン2019, Nov. 2019, Poster presentation

Existence of traveling wave solutions to a nonlocal equation with sign-changing kernel
Hiroshi ISHII
China-Japan Workshop for Young Researchers on Nonlinear Diffusion Equations, Oct. 2019, English, Invited oral presentation
[Invited]

反応拡散ネットワークに基づく本質的積分核の導出と分化の波への応用
栄伸一郎; 石井宙志; 近藤滋; 三浦岳; 田中吉太郎
日本数理生物学会, Sep. 2019, Poster presentation

Existence of traveling waves to a nonlocal scalar equation with sign-changing kernel
石井宙志
北海道大学偏微分方程式セミナー, Sep. 2019, Invited oral presentation
[Invited]

符号変化が伴う積分核を有する時間発展方程式における進行波解の存在
石井宙志
第13回応用数理研究会, Sep. 2019, Oral presentation

符号変化が伴う非局所分散項を持つFisher-KPP方程式における進行波解の存在について
石井宙志
第41回若手発展方程式セミナー, Aug. 2019, Oral presentation

Existence of traveling waves to a nonlocal scalar equation with sign-changing kernel
Hiroshi Ishii
Mini Workshop of Dynamics of localized patterns for reaction-diffusion systems and related topics, Aug. 2019, English, Invited oral presentation
[Invited]

球面上における分化の波の数値計算
石井宙志; 栄伸一郎; 佐藤純; 八杉徹雄
第15回数学総合若手研究集会, Mar. 2019, Poster presentation

分化の波のモデルと球面上への拡張
石井宙志
第1回次世代萌芽を育む現象と数理：生命とパターン形成, Mar. 2019, Japanese, Oral presentation

分化の波の数理モデルとその球面上への拡張
石井宙志; 栄伸一郎
反応拡散系と実験の融合2, Feb. 2019, Japanese, Invited oral presentation
[Invited]

Interacting pulses in a coupling system of RDEs with conservation law
Hiroshi Ishii; Tsubasa Sukekawa; Shin-Ichiro Ei
The 19th northeastern symposium on mathematical analysis, Feb. 2018, English, Poster presentation

微分積分学Ⅰ, 2024年, 学士課程, 全学教育

数理科学演習, 2024年, 学士課程, 理学部

Apr. 2022 - Present
JSIAM

Apr. 2020 - Present
日本数学会

Apr. 2018 - Present
日本数理生物学会

Mathematical analysis of cell sorting phenomenon
Grants-in-Aid for Scientific Research
01 Apr. 2024 - 31 Mar. 2029
村川 秀樹; 野津 裕史; 石井 宙志; 佐藤 純; 田中 吉太郎; 富樫 英
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (A), Ryukoku University, 24H00188

New development of pattern dynamics in reaction-diffusion equations on metric graphs
Grants-in-Aid for Scientific Research
01 Apr. 2025 - 31 Mar. 2028
森田 善久; 石井 宙志
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Ryukoku University, 25K07142

非局所反応拡散方程式のパターン形成における積分核形状の影響の解析
科学研究費助成事業 若手研究
Apr. 2023 - Mar. 2028
石井 宙志
日本学術振興会, 若手研究, 京都大学, 23K13013

The analysis of evolution of the spatial pattern for nonlocal reaction-diffusion equations
Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows
Apr. 2021 - Mar. 2023
石井 宙志
今年度はまず，非局所効果が十分小さい場合に非局所反応拡散方程式の空間パターンがどのように時間変化するか考察した．ある仮定の下では複数のフロント型局在パターンの重ね合わせで近似可能な時間発展する解の存在を示し，それぞれの局在パターンの位置の時間発展を積分核の不定積分を含む常微分方程式によって特徴づけすることに成功した．この結果により積分核の与え方によって多様な解の挙動が現れることを数学的に厳密に示すことができた．現在は仮定をより一般化することを試みている．
また，単独の局在パターンについての数理解析も進めており，存在や安定性の他に局在パターンの性質を数理モデルに含まれるパラメータで特徴づけすることを試みている．この研究で得られた形式的な結果の一部は，共同研究で提案された数理モデルに対する数理解析の結果としてまとめ，学術論文として投稿中である．
次に，反応拡散ネットワークから形式的に導出される，ネットワークの情報が縮約された非局所効果を持つ数理モデルを導出するEffective nonlocal kernelを用いたモデリング手法の数学的妥当性について考察を行った．ある特定の条件を満たす反応拡散ネットワークから定まる線形の非局所反応拡散方程式の解は，十分時間が立てば情報が縮約された数理モデルの解に収束することを明らかにした．今後はより一般的な仮定の下で妥当性を示し，モデリングへの応用に向けた解析を行っていく．
さらに，縮約された方程式の解の挙動の考察，および非局所効果による空間伝搬について考察するために，空間2階微分で記述される拡散方程式と畳み込み積分で記述される非局所拡散方程式の解の零点の漸近挙動について解析した．これら2つの方程式の場合には零点集合の上界や零点の漸近挙動で違いが現れることを明らかにした．これらの成果の一部は研究集会で発表するとともに，学術論文として投稿中である．
Japan Society for the Promotion of Science, Grant-in-Aid for JSPS Fellows, Hokkaido University, 21J10036

非線形現象の数値シミュレーションと解析 2026
04 Mar. 2026 - 05 Mar. 2026
Planning etc, Panel chair etc
Academic society etc
石井宙志，神保秀一，長山雅晴，森田善久

ReaDiNet 2025: International Conference on Recent Topics in Reaction-Diffusion Systems and Their Applications
01 Apr. 2025 - 31 Oct. 2025
Planning etc
Academic society etc

非線形現象の数値シミュレーションと解析 2025
03 Mar. 2025 - 04 Mar. 2025
Planning etc, Panel chair etc
Academic society etc
石井宙志、神保秀一、長山雅晴、森田善久
42269740

RIES international symposium 2024 Organizing member
01 Apr. 2024 - 10 Dec. 2024
Planning etc
Competition etc
Hokkaido University RIES

Mathematics in biological pattern formation problems
23 Aug. 2023
Planning etc, Panel chair etc
Competition etc
Shin-Ichiro Ei, Hiroshi Ishii

Methods and Applications in Mathematical Life Sciences
17 Feb. 2023
Planning etc, Panel chair etc
Academic society etc
Antoine Diez, Hiroshi Ishii, Clément Moreau

日本応用数理学会2022年度年会 正会員OS「複雑系における発生・発展現象の数理」
09 Sep. 2022
Planning etc, Panel chair etc
Competition etc
Antoine Diez, 石井宙志

第18回数学総合若手研究集会 世話人
Planning etc
Academic society etc

第17回数学総合若手研究集会 世話人
Planning etc
Academic society etc

第16回数学総合若手研究集会（Covid-19により中止） 世話人
Planning etc
Academic society etc

電子科学研究所一般公開「歯磨き粉で動く船を作ろう」
07 Jun. 2025 - 07 Jun. 2025
Planner
北海道大学 電子科学研究所