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Affiliation |
Engineering educational research section Science Center for Engineering Education |
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Title |
Associate Professor |
KOBAYASHI Shunsuke
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Degree 【 display / non-display 】
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理学 ( 2020.3 明治大学 )
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理学 ( 2017.3 明治大学 )
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理学 ( 2015.3 明治大学 )
Papers 【 display / non-display 】
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An instability framework of Hopf–Turing–Turing singularity in 2-component reaction–diffusion systems Reviewed
Izuhara H., Kobayashi S.
Japan Journal of Industrial and Applied Mathematics 42 ( 1 ) 63 - 112 2025.1
Publishing type：Research paper (scientific journal) Publisher：Japan Journal of Industrial and Applied Mathematics
This paper investigates pattern formation in 2-component reaction–diffusion systems with linear diffusion and local reaction terms. We propose a novel instability framework characterized by 0-mode Hopf instability, m and m + 1 mode Turing instabilities in 2-component reaction–diffusion systems. A normal form for the codimension 3 bifurcation is derived via the center manifold reduction, representing one of the main results in this paper. Additionally, we present numerical results on the bifurcation of certain reaction–diffusion systems and on the chaotic behavior of the normal form.
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Derivation of a curvature-dependent Kuramoto--Sivashinsky equation Reviewed
Shunsuke Kobayashi and Shigetoshi Yazaki
Proceedings of The Conference Algoritmy 189 - 198 2024.9
Authorship：Corresponding author Language：English Publishing type：Research paper (international conference proceedings)
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A new instability framework in 2-component reaction-diffusion system
Hirofumi Izuhara, Shunsuke Kobayashi
arXiv 2023.11
Authorship：Corresponding author Language：English Publishing type：Research paper (other academic)
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Kobayashi S., Yazaki S.
Computational Methods in Applied Mathematics 23 ( 2 ) 545 - 563 2022.11
Authorship：Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Computational Methods in Applied Mathematics
In this paper, we propose a finite difference scheme combined with the Crank-Nicolson-type discretization of the Kuramoto-Sivashinsky equation defined on an expanding circle, and show the existence, uniqueness, and second-order error estimate of the scheme. The equation is obtained as a perturbed graph equation from the circle solution to an interfacial curvature-dependent equation. The graph representation can provide guidelines for understanding the wavenumber selection of solutions to the interfacial equation. Indeed, the linearized stability analysis shows a relation between the parameters and the wavenumbers. Our proposed scheme can realize the relation with second-order accuracy.
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Spatio-temporal coexistence in the cross-diffusion competition system Reviewed
Izuhara H., Kobayashi S.
Discrete and Continuous Dynamical Systems - Series S 14 ( 3 ) 909 - 933 2021.3
Authorship：Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Discrete and Continuous Dynamical Systems - Series S
We study a two component cross-diffusion competition system which describes the population dynamics between two biological species. Since the cross-diffusion competition system possesses the so-called population pressure effects, a variety of solution behaviors can be exhibited compared with the classical diffusion competition system. In particular, we discuss on the existence of spatially non-constant time periodic solutions. Applying the center manifold theory and the standard normal form theory, the cross-diffusion competition system is reduced to a two dimensional dynamical system around a doubly degenerate point. As a result, we show the existence of stable time periodic solutions in the system. This means spatio-temporal coexistence between two biological species.
Books 【 display / non-display 】
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京大式サイエンスの創り方：狙ってもできないことがある
京都大学大学院理学研究科MACS教育プログラム実行委員会（ Role： Edit）
京都大学学術出版会 2022.4
Language：Japanese Book type：Scholarly book
MISC 【 display / non-display 】
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薄い固体上における燃焼現象に対する数理解析と火炎伝播速度の制御の可能性
小林 俊介
システム／制御／情報 68 ( 9 ) 356 - 361 2024.9
Authorship：Lead author, Corresponding author Language：Japanese Publishing type：Article, review, commentary, editorial, etc. (other)
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ネットワーク上でのパターン発生の機構
小林 俊介
数学セミナー 2024.2
Authorship：Lead author Publishing type：Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)
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蛇腹折りろ紙上の燃え拡がりの数理解析
小林 俊介，宮本 平，桑名 一徳，鳥飼 宏之，矢崎 成俊
Proceedings of JAFSE Annual Symposium 2023 2023.5
Authorship：Lead author Language：Japanese Publishing type：Research paper, summary (national, other academic conference)
Presentations 【 display / non-display 】
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コンパクトなメトリックグラフ上における Turing パターンと Wave パターン Invited
小林 俊介
北陸応用数理研究会2025 2025.2.20
Event date： 2025.2.20 - 2025.2.22
Language：Japanese Presentation type：Oral presentation (invited, special)
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Turing patterns and wave patterns on metric graphs Invited
Shunsuke Kobayashi
Reaction-Diffusion Equations and Nonlinear Dispersive Equations 2025.2.13
Event date： 2025.2.12 - 2025.2.14
Language：English Presentation type：Oral presentation (invited, special)
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空間依存性をもつ Kuramoto–Sivashinsky 方程式に対する有限差分法 Invited
小林 俊介
数学と現象 in 清里 2025.2.4
Event date： 2025.2.2 - 2025.2.4
Language：Japanese Presentation type：Oral presentation (invited, special)
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いくつかのコンパクトメトリックグラフ上における Turing パターンと Wave パターン Invited
小林 俊介
第4回 富山応用数学セミナー 2025.1.10
Event date： 2025.1.10
Language：Japanese Presentation type：Oral presentation (invited, special)
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ジャンクションをもつメトリックグラフ上での Turing パターン Invited
小林 俊介
数学と現象 in 伊香保 2024.9.1
Event date： 2024.8.30 - 2024.9.1
Language：Japanese Presentation type：Oral presentation (invited, special)
Awards 【 display / non-display 】
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Excellent Research Award
2019.3 The 10th Taiwa-Japan Joint Workshop for Young Scholars in Applied Mathematics The existence of rotating wave of a flame/smoldering-front evolution equation
Shunsuke Kobayashi
Award type：Award from international society, conference, symposium, etc.
Grant-in-Aid for Scientific Research 【 display / non-display 】
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固体可燃物の形状を考慮した燃焼モデルの確立ならびに防災へ向けた応用可能性の開拓
Grant number：24K16964 2024.04 - 2027.03
独立行政法人日本学術振興会 科学研究費基金 若手研究
Authorship：Principal investigator
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円形燻り燃焼に現れるパターンダイナミクスの解明へ向けた数理モデリングと数理解析
Grant number：20K22307 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 研究活動スタート支援
Authorship：Principal investigator