Construction of reaction-diffusion systems suitable to track interfacial dynamics

• Project/Area Number: 20540200
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: University of Miyazaki
• Principal Investigator: IIDA Masato University of Miyazaki, 工学部, 教授 (00242264)
• Co-Investigator(Kenkyū-buntansha): TSUJIKAWA Tohru 宮崎大学, 工学部, 教授 (10258288) ; OHTSUKA Hiroshi 宮崎大学, 工学部, 准教授 (20342470) ; YAZAKI Shigetoshi 宮崎大学, 工学部, 准教授 (00323874)
• Co-Investigator(Renkei-kenkyūsha): NINOMIYA Hirokazu 明治大学, 理工学部, 准教授 (90251610)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 反応拡散系 / 特異摂動 / 界面ダイナミクス / 国際情報交換 / 米国 / フランス:米国

Research Abstract

Some free boundary problems describing the spatial segregation of competitive species can be regarded as certain singular limits of some reaction-diffusion systems. The mathematical grounds of this fact have been obtained. It is also shown that a mathematical model describing multi-phase invasion of cooperative species can be approximated by stacked fronts of several Fisher's waves which are mathematical models describing the single invasion of a species.

Research Products

• [Journal Article] Stacked fronts for cooperative systems with equal diffusion coefficients (2011)
  • Author(s): M.Iida, R.Lui, H.Ninomiya
  • Journal Title: SIAM Journal on Mathematical Analysis Vol.43 Pages: 1369-1389
  • Peer Reviewed
• [Journal Article] Asymptotic non-degeneracy of the multiple blow-up solutions to the Gel'fand problem in two space dimensions (2011)
  • Author(s): M.Grossi, H.Ohtsuka, T.Suzuki
  • Journal Title: Advances in Differential Equations Vol.16 Pages: 145-164
  • Peer Reviewed
• [Journal Article] Stationary patterns for an adsorbated-induced phase transition model I : Existence (2010)
  • Author(s): K.Kuto, T.Tsujikawa
  • Journal Title: Discrete Conti.Dynam.Systems B14 Pages: 1105-1117
  • Peer Reviewed
• [Journal Article] Blow-up analysis for an elliptic equation describing stationary vortex flows with variable intensities in 2D-turbulence (2010)
  • Author(s): H.Ohtsuka, T.Ricciardi, T.Suzuki
  • Journal Title: J.Differ.Equ. Vol.249 Pages: 1436-1465
  • NAID: 130004604346
  • Peer Reviewed
• [Journal Article] Shadow system for adsorbate-induced phase transition model (2009)
  • Author(s): K.Kuto, T.Tsujikawa
  • Journal Title: RIMS Kokuroku Bessatsu B15 Pages: 1-14
  • Peer Reviewed
• [Journal Article] Stationary solutions to forest kinematic model (2009)
  • Author(s): L.H.Chuan, T.Tsujikawa, A.Yagi
  • Journal Title: Glasgow Math.J Vol.51 Pages: 1-17
  • NAID: 120005249166
  • Peer Reviewed
• [Journal Article] Second order numerical scheme for motion of polygonal curves with constant area speed (2009)
  • Author(s): M.Benes, M.Kimura, S.Yazaki
  • Journal Title: Interfaces and Free Boundaries Vol.11 Pages: 515-536
  • Peer Reviewed
• [Journal Article] Relative compactness in L^p of solutions of some 2m components competition-diffusion systems (2008)
  • Author(s): D.Hilhorst, M.Iida, M.Mimura, H.Ninomiya
  • Journal Title: Discrete and Conti.Dynam.Systems Vol.21 Pages: 233-244
  • Peer Reviewed
• [Journal Article] Application of a curvature adjusted method in image segmentation, Bulletin of the Institute of Mathematics (2008)
  • Author(s): M.Benes, M.Kimura, P.Paus, D.Sevcovic, T.Tsujikawa, S.Yazaki
  • Journal Title: Academia Sinica, New Series Vol.3
  • Peer Reviewed
• [Journal Article] Relative compactness in Lp of solutions of some 2m components competition-diffusion systems (2008)
  • Author(s): D. Hilhorst, M. Iida, M. Mimura, H. Ninomiya
  • Journal Title: Discrete and Continuous Dynamical Sys tems Vol. 21 N0. 1 Pages: 233-244
  • Peer Reviewed
• [Journal Article] Stacked fronts for cooperative systems with equal diffusion coefficients
  • Author(s): Masato Iida, Roger Lui, Hirokazu Ninomiya
  • Journal Title: SIAM Journal on Mathematical Analysis Volume: (In press)
  • Peer Reviewed
• [Presentation] 点渦系のHamiltonianとその平衡平均場の変分構造について (2011)
  • Author(s): 大塚浩史
  • Organizer: 第3回福島応用数学研究集会
  • Place of Presentation: コラッセ福島
  • Year and Date: 2011-03-11
• [Presentation] Bifurcation structure of stationary solutions for the reaction-diffusion-advection system (2011)
  • Author(s): T.Tsujikawa
  • Organizer: 第28回九州における偏微分方程式研究集会
  • Place of Presentation: 九州大学
  • Year and Date: 2011-01-26
• [Presentation] 個体群の多段階侵入の定式化-協調拡散系の場合- (2011)
  • Author(s): 飯田雅人
  • Organizer: 研究集会「拡散と移流の数理」
  • Place of Presentation: 別府亀の井ホテル由布の間
  • Year and Date: 2011-01-19
• [Presentation] 個体群の多段階侵入の定式化-協調拡散系の場合- (2011)
  • Author(s): 飯田雅人
  • Organizer: 拡散と移流の数理
  • Place of Presentation: 別府亀の井ホテル由布の間
  • Year and Date: 2011-01-19
• [Presentation] On multi-phase invasions in a Lotoka-Volterra cooperative system with diffusion (2010)
  • Author(s): 飯田雅人
  • Organizer: Nonlinear Analysis and Integrable Systems
  • Place of Presentation: 龍谷大学セミナーハウス「ともいき荘」
  • Year and Date: 2010-11-19
• [Presentation] On multi-phase invasions in a Lotka-Volterra cooperative system with diffusion (2010)
  • Author(s): Masato Iida
  • Organizer: Nonlinear Analysis and Integrable Systems
  • Place of Presentation: 龍谷大学セミナーハウス「ともいき荘」
  • Year and Date: 2010-11-19
• [Presentation] On motion of curves in the plane (2010)
  • Author(s): 矢崎成俊
  • Organizer: Nonlinear evolution equations and related topics to mathematical analysis of a phenomena
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-10-14
• [Presentation] Numerical study on Hele-Shaw flows in a time-dependent gap (2010)
  • Author(s): 矢崎成俊
  • Organizer: Czech-Japanese Seminar in Applied Mathematics
  • Place of Presentation: Lecture Hall CVUT at Telc, Czech Republic
  • Year and Date: 2010-09-03
• [Presentation] Stationary patterns of a reaction-diffusion-advection system (2010)
  • Author(s): T.Tsujikawa
  • Organizer: Czech-Japan Seminar in Applied Mathematics 2010
  • Place of Presentation: Czech Technical University in Prague
  • Year and Date: 2010-08-30
• [Presentation] Topics related to multi-phase invasions in population dynamics (2010)
  • Author(s): 飯田雅人
  • Organizer: Nonlinear Evolutionary PDEs and their Equilibrium States
  • Place of Presentation: 早稲田大学理工学部
  • Year and Date: 2010-06-11
• [Presentation] On the variational structure of the Gel'fand problem (2010)
  • Author(s): 大塚浩史
  • Organizer: 京都大学数理解析研究所研究集会「変分問題の展開-幾何学的勾配流と臨界点理論の新潮流-」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-06-08
• [Presentation] Various gradient flows in the plane-modeling, applications and polygonal analogues (2010)
  • Author(s): 矢崎成俊
  • Organizer: Progress in variational problems--New trends of geometric gradient flow and critical point theory
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-06-07
• [Presentation] 点渦系とその平均場について (2010)
  • Author(s): 大塚浩史
  • Organizer: 日本数学会2010年度年会(函数方程式論分科会特別講演)
  • Place of Presentation: 慶應義塾大学矢上キャンパス
  • Year and Date: 2010-03-25
• [Presentation] ある半線形楕円型方程式の正値解の無限遠での漸近挙動とその応用 (2010)
  • Author(s): 飯田雅人
  • Organizer: 第67回解析セミナー
  • Place of Presentation: 愛媛大学理学部
  • Year and Date: 2010-01-23
• [Presentation] 反応拡散系の急速反応極限によって見えるもの (2009)
  • Author(s): 飯田雅人
  • Organizer: 日本数学会秋季総合分科会(函数方程式論分科会特別講演)
  • Place of Presentation: 大阪大学豊中キャンパス
  • Year and Date: 2009-09-26
• [Presentation] 反応拡散系の急速反応極限によって見えるもの(函数方程式論分科会特別講演) (2009)
  • Author(s): 飯田雅人
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学理学部
  • Year and Date: 2009-09-26
• [Presentation] Bifurcation structure of steady states in the shadow system for the adsorbate-induced phase transition model (2009)
  • Author(s): T.Tsujikawa
  • Organizer: Conference on "Evolution equations, Related Topics and Applications"
  • Place of Presentation: Helmholtz Zentrum munichen, Germany
  • Year and Date: 2009-09-10
• [Presentation] ある反応拡散系の角遷移層における漸近解の構成 (2009)
  • Author(s): 飯田雅人
  • Organizer: 九州関数方程式セミナー
  • Place of Presentation: 福岡大学セミナーハウス
  • Year and Date: 2009-07-17
• [Presentation] Evolution of plane curves and its numerical computations (2009)
  • Author(s): 矢崎成俊
  • Organizer: Algoritmy 2009
  • Place of Presentation: Podbanske
  • Year and Date: 2009-03-17
• [Presentation] 平面閉曲線の曲率流の導出とその数値計算 (2008)
  • Author(s): 矢崎成俊
  • Organizer: 盛岡応用数学小研究集会
  • Place of Presentation: 岩手大学
  • Year and Date: 2008-12-13
• [Presentation] 個体群侵入における段階別侵入速度について (2008)
  • Author(s): 飯田雅人
  • Organizer: 盛岡応用数学小研究集会
  • Place of Presentation: 岩手大学
  • Year and Date: 2008-12-13
• [Presentation] 平面曲線の曲率流方程式とその数値計算について (2008)
  • Author(s): 矢崎成俊
  • Organizer: 第10回界面ダイナミクスと数値シミュレーション
  • Place of Presentation: 神戸インスティチュート
  • Year and Date: 2008-11-29
• [Presentation] Global structure of stationary solutions of shadow system for adsorbate-induced phase transition model (2008)
  • Author(s): T.Tsujikawa
  • Organizer: Czech-Japan Seminar in Applied Mathematics 2008
  • Place of Presentation: 宮崎大学
  • Year and Date: 2008-09-07
• [Presentation] 曲率の大きさを鑑みた接線速度を持つ平面曲線の時間発展方程式の数値計算について (2008)
  • Author(s): 矢崎成俊
  • Organizer: 第2回岐阜非線形ワークショップ
  • Place of Presentation: 岐阜大学
  • Year and Date: 2008-07-30
• [Presentation] Asymptotic non-degeneracy results for the mean field equations on surfaces (2008)
  • Author(s): 大塚浩史
  • Organizer: 京都大学数理解析研究所研究集会「変分問題とその周辺」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-06-23
• [Book] Topics in mathematical modeling, Part 4(An area-preserving crystalline curvature flow equation)(eds : M.Benes, E.Feireisl)Vol.4, matfyzpress (2008)
  • Author(s): S.Yazaki
  • Publisher: Jindrich Necas center for mathematical modeling lecture notes