Mechanism of spatiotemporal patterns generated by reaction-diffusion systems

• Project/Area Number: 20740087
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Tohoku University
• Principal Investigator: SUZUKI Kanako Tohoku University, 国際高等研究教育機構, 助教 (10451519)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 非線形現象 / 反応拡散系 / パターン形成

Research Abstract

This study is concerned with the dynamics of reaction-diffusion systems modeling pattern formation in biological phenomena. I considered the role of parameters in reaction-diffusion systems on its dynamics. Concerning an activator-inhibitor system, the mechanism of "collapse of patterns" could be understood. I also considered one-dimensional chemotaxis equations to study the asymptotic behavior of solutions, and three component reaction-diffusion equations to show the existence and stability of spatial patterns.

Research Products

• [Journal Article] Blow-up versus global existence of solutions to aggregation equations (2011)
  • Author(s): Grzegorz Karch, Kanako Suzuki
  • Journal Title: Applicationes Mathematicae 掲載決定
  • Peer Reviewed
• [Journal Article] On the role of basic production terms in an activator-inhibitor system modeling biological pattern formation (2011)
  • Author(s): Kanako Suzuki, Izumi Takagi
  • Journal Title: Funkcialaj Ekvacio 掲載決定
  • NAID: 130000953648
  • Peer Reviewed
• [Journal Article] On the role of basic production terms in an activator-inhibitor system modeling biological pattern formation (2011)
  • Author(s): Kanako Suzuki, Izumi Takagi
  • Journal Title: Funkcialaj Ekvacioj Volume: (未定 掲載決定)
  • NAID: 130000953648
  • Peer Reviewed
• [Journal Article] Blow-up versus global existence of solutions to aggregation equations (2011)
  • Author(s): Grzegorz Karch, Kanako Suzuki
  • Journal Title: Applicationes Mathematicae Volume: (未定 掲載決定)
  • Peer Reviewed
• [Journal Article] Spikes and diffusion waves in a one-dimensional model of chemotaxis (2010)
  • Author(s): Grzegorz Karch, Kanako Suzuki
  • Journal Title: Nonlinearity 23巻 Pages: 3119-3137
  • Peer Reviewed
• [Journal Article] Collapse of patterns and effect of basic production terms in some reaction-diffusion systems (2010)
  • Author(s): Kanako Suzuki, Izumi Takagi
  • Journal Title: GAKUTO international series "Current Advances in Nonlinear Analysis and Related Topics" Mathematical Sciences and Applications 32巻 Pages: 163-187
• [Journal Article] Spikes and diffusion waves in a one-dimensional model of chemotaxis (2010)
  • Author(s): Grzegorz Karch, Kanako Suzuki
  • Journal Title: Nonlinearity Volume: 23 Pages: 3119-3137
  • Peer Reviewed
• [Journal Article] Collapse of patterns and effect of basic production terms in some reaction-diffusion systems (2010)
  • Author(s): 鈴木香奈子、高木泉
  • Journal Title: GAKUTO international series "Current Advances in Nonlinear Analysis and Related Topics" Mathematical Sciences and Applications Vol.32(掲載決定)
• [Journal Article] Behavior of solutions to an activator-inhibitor system with basic production terms, Proceedings of Czech-Japanese Seminar in Applied Mathematics 2008 (2009)
  • Author(s): Kanako Suzuki, Izumi Takagi
  • Journal Title: COE Lect.Note, Kyushu Univ.Global COE Program, Fukuoka 14巻 Pages: 49-59
  • Peer Reviewed
• [Journal Article] Behavior of solutions to an activator-inhibitor system with basic production terms (2009)
  • Author(s): 鈴木香奈子, 高木泉
  • Journal Title: Proceedings of Czech-Japanese Seminar in Applied Mathematics 2008, COE Lect. Note, Kyushu Univ. Global COE Program. Fukuoka 14 Pages: 49-59
  • NAID: 120006654389
  • Peer Reviewed
• [Presentation] Asymptotic behaviour of solutions to one-dimensional nonlocal transport equation (2011)
  • Author(s): Kanako Suzuki
  • Organizer: International Winter School "Mathematical Analysis of Fluid Mechanics"
  • Place of Presentation: ポーランド
  • Year and Date: 2011-02-08
• [Presentation] Asymptotic behaviour of solutions to one-dimensional nonlocal transport equation (2011)
  • Author(s): 鈴木香奈子
  • Organizer: International Winter School"Mathematical Analysis of Fluid Mechanics"
  • Place of Presentation: Bialka Tatrzanska(ポーランド)
  • Year and Date: 2011-02-08
• [Presentation] Existence and behavior of solutions to aggregation equations (2011)
  • Author(s): Kanako Suzuki
  • Organizer: The 6^<th> Jikji Workshop : Infinite Dimensional Analysis and Quantum Probability
  • Place of Presentation: 韓国
  • Year and Date: 2011-01-11
• [Presentation] Existence and behavior of solutions to aggregation equations (2011)
  • Author(s): 鈴木香奈子
  • Organizer: The 6^<th> Jikji Workshop : Infinite Dimensional Analysis and Quantum Probability
  • Place of Presentation: NIMS(韓国)
  • Year and Date: 2011-01-11
• [Presentation] 凝集現象を記述する方程式の解の漸近挙動 (2010)
  • Author(s): 鈴木香奈子
  • Organizer: 松山数学小研究会-Matsuyama Mini Workshop on Pure and Applied Mathematics-
  • Place of Presentation: 愛媛大学
  • Year and Date: 2010-12-05
• [Presentation] 凝集現象を記述する方程式の解の漸近挙動 (2010)
  • Author(s): 鈴木香奈子
  • Organizer: 松山数学小研究会-Matsuyama Mini Workshop on Pure and Applied Mathematics-
  • Place of Presentation: 愛媛大学理学部(愛媛県)
  • Year and Date: 2010-12-05
• [Presentation] 一次元走化性モデルの解の時間大域的挙動 (2010)
  • Author(s): 鈴木香奈子
  • Organizer: 仙台楕円型・放物型微分方程式研究集会
  • Place of Presentation: 東北大学
  • Year and Date: 2010-12-03
• [Presentation] 一次元走化性モデルの解の時間大域的挙動 (2010)
  • Author(s): 鈴木香奈子
  • Organizer: 仙台 楕円型・放物型微分方程式研究集会
  • Place of Presentation: 東北大学理学部合同棟801号室(宮城県)
  • Year and Date: 2010-12-03
• [Presentation] 発癌メカニズムを記述するある反応拡散系が見せる空間パターン (2010)
  • Author(s): 鈴木香奈子
  • Organizer: 数学の展開-諸分野との連携を探る
  • Place of Presentation: 東北大学
  • Year and Date: 2010-11-27
• [Presentation] 発癌メカニズムを記述するある反応拡散系が見せる空間パターン (2010)
  • Author(s): 鈴木香奈子
  • Organizer: 数学の展開--諸分野との連携を探る
  • Place of Presentation: 東北大学理学部化学第4講義棟(宮城県)
  • Year and Date: 2010-11-27
• [Presentation] Patterns of the shadow system with nontrivial basic production terms (2010)
  • Author(s): Kanako Suzuki
  • Organizer: Concentration and Related Topics on Nonlinear Problems
  • Place of Presentation: 東北大学
  • Year and Date: 2010-11-22
• [Presentation] Patterns of the shadow system with nontrivial basic production terms (2010)
  • Author(s): 鈴木香奈子
  • Organizer: Concentration and Related Topics on Nonlinear Problems
  • Place of Presentation: 東北大学川井ホール(宮城県)
  • Year and Date: 2010-11-22
• [Presentation] Patterns in a reaction-diffusion model of early carcinogenesis (2010)
  • Author(s): Kanako Suzuki
  • Organizer: Mini-Workshop on Modeling, Simulations and Analysis of Biological Pattern Formation
  • Place of Presentation: 宮城県仙台市
  • Year and Date: 2010-10-30
• [Presentation] Patterns in a reaction-diffusion model of early carcinogenesis (2010)
  • Author(s): 鈴木香奈子
  • Organizer: Mini-Workshop on Modeling, Simulations and Analysis of Biological Pattern Formation
  • Place of Presentation: ハーネル仙台4階会議室(宮城県)
  • Year and Date: 2010-10-30
• [Presentation] Steady-state patterns of the shadow system with nontrivial basic production terms (2010)
  • Author(s): Kanako Suzuki
  • Organizer: Partial Differential Equations in Mathematical Biology
  • Place of Presentation: ポーランド
  • Year and Date: 2010-09-13
• [Presentation] Steady-state patterns of the shadow system with nontrivial basic production terms (2010)
  • Author(s): 鈴木香奈子
  • Organizer: Partial Differential Equations in Mathematical Biology
  • Place of Presentation: Mathematical Research and Conference Center(ポーランド)
  • Year and Date: 2010-09-13
• [Presentation] Spikes and diffusion waves in one-dimensional model of chemotaxis (2010)
  • Author(s): Kanako Suzuki
  • Organizer: Nonlocal operators and partial differential equations
  • Place of Presentation: ポーランド
  • Year and Date: 2010-06-29
• [Presentation] Spikes and diffusion waves in one-dimensional model of chemotaxis (2010)
  • Author(s): 鈴木香奈子
  • Organizer: Nonlocal operators and partial differential equations
  • Place of Presentation: Mathematical Research and Conference Center(ポーランド)
  • Year and Date: 2010-06-29
• [Presentation] ある活性因子-抑制因子系におけるパターンの崩壊現象 (2010)
  • Author(s): 鈴木香奈子
  • Organizer: 第7回城崎新人セミナー
  • Place of Presentation: 兵庫県
  • Year and Date: 2010-02-17
• [Presentation] ある活性因子-抑制因子系におけるパターンの崩壊現象 (2010)
  • Author(s): 鈴木香奈子
  • Organizer: 第7回城崎新人セミナー
  • Place of Presentation: 城崎健康福祉センター(兵庫県)
  • Year and Date: 2010-02-17
• [Presentation] 基礎生産項を含むある活性因子-抑制因子系におけるパターンの崩壊 (2010)
  • Author(s): 鈴木香奈子
  • Organizer: 京都駅前セミナー
  • Place of Presentation: 京都府
  • Year and Date: 2010-01-22
• [Presentation] 基礎生産項を含むある活性因子-抑制因子系におけるパターンの崩壊 (2010)
  • Author(s): 鈴木香奈子
  • Organizer: 京都駅前セミナー
  • Place of Presentation: キャンパスプラザ京都(京都府)
  • Year and Date: 2010-01-22
• [Presentation] 基礎生産項を含むギーラー・マインハルト系におけるパターンの崩壊 (2009)
  • Author(s): 鈴木香奈子
  • Organizer: 数理解析セミナー
  • Place of Presentation: 首都大学東京
  • Year and Date: 2009-12-03
• [Presentation] 基礎生産項を含むギーラー・マインハルト系におけるパターンの崩壊 (2009)
  • Author(s): 鈴木香奈子
  • Organizer: 数理解析セミナー
  • Place of Presentation: 首都大学東京(東京都)
  • Year and Date: 2009-12-03
• [Presentation] 空間非一様な基礎生産項を含むある反応拡散系の定常解について (2009)
  • Author(s): 鈴木香奈子
  • Organizer: 若手のための偏微分方程式と数学解析
  • Place of Presentation: 九州大学
  • Year and Date: 2009-02-20
• [Presentation] 空間非一様な基礎生産項を含むある反応拡散系の定常解について (2009)
  • Author(s): 鈴木香奈子
  • Organizer: 若手のための偏微分方程式と数学解析
  • Place of Presentation: 福岡九州大学西新プラザ
  • Year and Date: 2009-02-20
• [Presentation] ギーラー・マインハルト系の解と空間不均一なパラメータとの関係 (2009)
  • Author(s): 鈴木香奈子
  • Organizer: 九州非線形数理集中・力学系合同セミナー
  • Place of Presentation: 福岡九州大学西新プラザ
  • Year and Date: 2009-02-20
• [Presentation] Collapse of spatial patterns in an activator-inhibitor system (2009)
  • Author(s): Kanako Suzuki
  • Organizer: The3^<rd> Cheongju Workshop on Infinite Dimensional Analysis and Quantum Probability
  • Place of Presentation: 韓国
  • Year and Date: 2009-01-12
• [Presentation] Collapse of spatial patterns in an activator-inhibitor system (2009)
  • Author(s): 鈴木香奈子
  • Organizer: The 3^<rd> Cheongju Workshop on Infinite Dimension al Analysis and Quantum Probability
  • Place of Presentation: 韓国, Chungbuk National University
  • Year and Date: 2009-01-12
• [Presentation] ギーラー・マインハルト系の解と空間不均一なパラメータとの関係 (2009)
  • Author(s): 鈴木香奈子
  • Organizer: 九州非線形数理集中・力学系合同セミナー
  • Place of Presentation: 九州大学
• [Presentation] Collapse of patterns in some reaction-diffusion systems and how to prevent it (2008)
  • Author(s): Kanako Suzuki
  • Organizer: 非線形問題に現れる特異性の解析
  • Place of Presentation: 京都府
  • Year and Date: 2008-12-02
• [Presentation] Collapse of patterns in some reaction-diffusion systems and how to prevent it (2008)
  • Author(s): 鈴木香奈子
  • Organizer: 非線形問題に現れる特異性の解析(Singularities arising in Nonhllear Problems 2008)
  • Place of Presentation: 京都関西セミナーハウス
  • Year and Date: 2008-12-02
• [Presentation] ある反応拡散方程式系の解のダイナミクス (2008)
  • Author(s): 鈴木香奈子
  • Organizer: 偏微分方程式と現象:PDEs and Phenomena in Miyazaki 2008
  • Place of Presentation: 宮崎大学
  • Year and Date: 2008-11-14
• [Presentation] ある反応拡散方程式系の解のダイナミクス (2008)
  • Author(s): 鈴木香奈子
  • Organizer: 偏微分方程式と現象 : PDEs and Phenomena in Miyazaki 2008
  • Place of Presentation: 宮崎大学工学部
  • Year and Date: 2008-11-14
• [Presentation] Behavior of solutions to an activator-inhibitor system with basic production terms (2008)
  • Author(s): Kanako Suzuki
  • Organizer: Czech-Japanese seminar in applied mathema tics 2008
  • Place of Presentation: 宮崎県
  • Year and Date: 2008-09-01
• [Presentation] Behavior of solutions to an activator-inhibitor system with basic Production terms (2008)
  • Author(s): 鈴木香奈子
  • Organizer: Czech-Japanese seminar in applied mathematics 2008
  • Place of Presentation: 宮崎県高千穂町五ケ村集落センター
  • Year and Date: 2008-09-01
• [Remarks] ホームページ等