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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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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.
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Analysis of Kuramoto-Sivashinsky Model of Flame/Smoldering Front by Means of Curvature Driven Flow Reviewed International coauthorship
Miroslav Kolar, Shunsuke Kobayashi, Yasuhide Uegata, Shigetoshi Yazaki, Michal Benes
Lecture Notes in Computational Science and Engineering 615 - 624 2020.8
Language：English Publishing type：Research paper (international conference proceedings)
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The existence of intrinsic rotating wave solutions of a flame/smoldering-front evolution equation Reviewed
Shunsuke Kobayashi, Yasuhide Uegata, Shigetoshi Yazaki
JSIAM Letters 12 53 - 56 2020.8
Authorship：Corresponding author Language：English Publishing type：Research paper (scientific journal)
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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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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Mathematical modeling and simulations to flame spreading on an accordion folded paper International conference
Shunsuke Kobayashi
ALGORITMY2024 2024.3.16
Event date： 2024.3.15 - 2024.3.20
Language：English Presentation type：Oral presentation (general)
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あるコンパクトなメトリックグラフ上における Turing 分岐と Wave 分岐 Invited
小林 俊介
研究集会「力学系に対する相空間全構造解析と分岐解析の統合による新たなアプローチ」 2024.2.16
Event date： 2024.2.16
Language：Japanese Presentation type：Oral presentation (invited, special)
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固体燃焼における燃焼波面の定性的理解へ向けた Kuramoto–Sivashinsky 方程 式の応用可能性 Invited
小林 俊介
MIMS 研究集会「広い意味での防災にまつわる実験数理融合アプローチの新展開」 2023.10.11
Event date： 2023.10.11 - 2023.10.12
Language：Japanese Presentation type：Oral presentation (invited, special)
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コンパクトなメトリックグラフ上における Turing 分岐と Wave 分岐 Invited
小林 俊介
数学と現象 in 伊豆 2023.8.29
Event date： 2023.8.28 - 2023.8.31
Language：Japanese Presentation type：Oral presentation (invited, special)
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Mathematical modeling of flame/smoldering front-evolution and its application International conference
Shunsuke Kobayashi
10th International Congress on Industrial and Applied Mathematics 2023.8.23
Event date： 2023.8.20 - 2023.8.25
Language：English Presentation type：Oral presentation (general)
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
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