Pattern formation arising in reaction-diffusion systems via variational methods

• Project/Area Number: 18740083
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Okayama University
• Principal Investigator: OSHITA Yoshihito Okayama University, 大学院・自然科学研究科, 准教授 (70421998)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,800,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,200,000 (Direct Cost: ¥1,200,000); Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
• Keywords: 変分法 / 非線形現象 / シャープインターフェース / 特異摂動 / 楕円型偏微分方程式 / 内部遷移層 / シャープインタフェース / 楕円型偏微分方程式系 / 活性因子・抑制因子型反応拡散系 / 遷移層 / 楕円形方程式 / 自由境界

Research Abstract

ある種の非線形偏微分方程式の解の構造に関する研究を行った.具体的には,活性因子・抑制因子型反応拡散方程式系の内部遷移層解の特異極限として現れる曲率依存型の界面方程式において,付随するエネルギー汎関数の変分解析とリャプノフ・シュミットの縮約法を組み合わせた手法により,領域の対称性を仮定せずに,連結で非対称非退化な解の存在を示し,さらに非線形楕円型偏微分方程式の解の線形化非退化性に関する研究を行った.

Research Products

• [Journal Article] Uniqueness of standing waves for nonlinear Schroedinger equations (2008)
  • Author(s): Jaeyoung Byeon and Yoshihito Oshita
  • Journal Title: Proc. Roy. Soc. Edinburgh Sect. A 138 Pages: 975-987
  • Peer Reviewed
• [Journal Article] Uniqueness of standing waves for nonlinear Schroedinger equations (2008)
  • Author(s): J. Byeon and Y. Oshita
  • Journal Title: Proc. Roy. Soc. Edinburgh Sect. A. 138 Pages: 975-987
  • Peer Reviewed
• [Journal Article] 応用数理 (2007)
  • Author(s): 大下承民
  • Journal Title: 活性因子・抑制因子型反応拡散系の特異極限問題とパターン形成 17 Pages: 215-226
  • Peer Reviewed
• [Journal Article] Singular limit problem for some elliptic systems (2007)
  • Author(s): Yoshihio Oshita
  • Journal Title: SIAM J. Math. Anal. 38 Pages: 1886-1911
  • Peer Reviewed
• [Journal Article] Singular limit problem for some elliptic systems (2007)
  • Author(s): 大下承民
  • Journal Title: 2006, Surikaiseki Kokyuroku No. 1528 Pages: 85-95
• [Journal Article] Singular limit problem for some elliptic systems (2007)
  • Author(s): Yoshihito Oshita
  • Journal Title: SIAM J. Math. Anal. 38 Pages: 1886-1911
  • Peer Reviewed
• [Journal Article] 活性因子・抑制因子型反応拡散系の特異摂動問題とパターン形成 (2007)
  • Author(s): 大下承民
  • Journal Title: 応用数理 17 Pages: 215-226
  • Peer Reviewed
• [Journal Article] An Application of the Modular Function in Nonlocal Variaticnal Problems (2007)
  • Author(s): X. Chen and Y. Oshita
  • Journal Title: Archive for rational Mechanics and Analysis 186 Pages: 109-132
  • Peer Reviewed
• [Journal Article] Singular limit problem for some elliptic systems (2007)
  • Author(s): 大下承民
  • Journal Title: 数理解析研究所講究録 1528 Pages: 85-95
• [Journal Article] Singular limit problem for some elliptic systems
  • Author(s): Yoshihito Oshita
  • Journal Title: SIAM J.Math.Anal. (予定)(確約有り)
• [Journal Article] 活性因子・抑制因子型反応拡散系の特異摂動問題とパターン形成
  • Author(s): 大下承民
  • Journal Title: 応用数理 (予定)(確約有り)
• [Presentation] Fine structures arising in diblock copolymers and reaction-diffusion systems (2008)
  • Author(s): Yoshihito Oshita
  • Organizer: OxPDE Seminar
  • Place of Presentation: University of Oxford
  • Year and Date: 2008-11-24
• [Presentation] Fine structures arising in diblock copolymers and reaction-diffusion systems (2008)
  • Author(s): Yoshihito Oshita
  • Organizer: OxPDE Seminar
  • Place of Presentation: Oxford
  • Year and Date: 2008-11-24
• [Presentation] Existence of multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations (2008)
  • Author(s): Yoshihito Oshita
  • Organizer: Variational Methods for Elliptic PDE's and Hamiltonian Systems
  • Place of Presentation: POSTECH
  • Year and Date: 2008-10-10
• [Presentation] Existence of multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations (2008)
  • Author(s): Yoshihito Oshita
  • Organizer: Variational Methods for Elliptic PDE's and Hamiltonian Systems
  • Place of Presentation: Pohang
  • Year and Date: 2008-10-10
• [Presentation] Hexagonal Patterns of Di-Block Copolymer Melts (2008)
  • Author(s): Yoshihito Oshita
  • Organizer: SIAM Conference on Mathematical Aspects of Materials Science
  • Place of Presentation: Philadelphia
  • Year and Date: 2008-05-12
• [Presentation] Singular limit problem for some elliptic systems (2008)
  • Author(s): Yoshihito Oshita
  • Organizer: Special Lecture
  • Place of Presentation: Pusan National University
  • Year and Date: 2008-03-28
• [Presentation] Singular limit problem for some elliptic systems (2008)
  • Author(s): Yoshihito Oshita
  • Organizer: 碩学特別講演会
  • Place of Presentation: 韓国 プサン
  • Year and Date: 2008-03-28
• [Presentation] 非線形楕円型方程式の正値解の非退化性とmulti-bump 解 (2008)
  • Author(s): 大下承民
  • Organizer: 非線形現象の数値シミュレーションと解析2008
  • Place of Presentation: 北海道大学
• [Presentation] Uniqueness of standing waves for nonlinear Schrodinger equations (2008)
  • Author(s): Yoshihito Oshita
  • Organizer: Young Asian Conference on Partial Differential Equations
  • Place of Presentation: POSTECH
• [Presentation] Singular limit problem for some elliptic systems (2007)
  • Author(s): Yoshihito Oshita
  • Organizer: SIAM Conference on analysis of Partial Differential Equation
  • Place of Presentation: 米国 メサ
  • Year and Date: 2007-12-10
• [Presentation] Singular limit problem for elliptic systems of activator-inhibitor type PDE seminar (2007)
  • Author(s): Yoshihito Oshita
  • Organizer: National Taiwan Normal University
  • Place of Presentation: Taipei
  • Year and Date: 2007-10-16
• [Presentation] Singular limit problem for elliptic elliptic systems of activator-inhibitor type (2007)
  • Author(s): Yoshihito Oshita
  • Organizer: PDE seminar
  • Place of Presentation: 台湾 Taipei
  • Year and Date: 2007-10-16
• [Presentation] Singular limit problem for some elliptic problems PDE seminar (2007)
  • Author(s): Yoshihito Oshita
  • Organizer: Pohang University of Science and Technology
  • Place of Presentation: Pohang
  • Year and Date: 2007-03-28
• [Presentation] Singular limit problems for some elliptic systems (2007)
  • Author(s): 大下承民
  • Organizer: SIAM Conference on Analysis of Partial Differential Equations (PD07)
  • Place of Presentation: Mesa
• [Presentation] Singularly perturbed nonlocal (2006)
  • Author(s): Yoshihito Oshita
  • Organizer: variational problem SNP 2006
  • Place of Presentation: 京都
  • Year and Date: 2006-12-05
• [Presentation] ある楕円型システムの特異極限問題 (2006)
  • Author(s): 大下承民
  • Organizer: 応用解析セミナー
  • Place of Presentation: 熊本
  • Year and Date: 2006-11-11
• [Presentation] ある楕円型システムの特異極限問題 (2006)
  • Author(s): 大下承民
  • Organizer: NSC12周年:非線形数理の現状と発展
  • Place of Presentation: 札幌
  • Year and Date: 2006-10-13
• [Presentation] ある楕円型システムの特異極限問題 (2006)
  • Author(s): 大下承民
  • Organizer: 非線型の諸問題
  • Place of Presentation: 別府
  • Year and Date: 2006-09-29
• [Presentation] 楕円型方程式系の特異極限問題 (2006)
  • Author(s): 大下承民
  • Organizer: 日本数学会
  • Place of Presentation: 大阪
  • Year and Date: 2006-09-21
• [Presentation] Singular limit problem for some elliptic systems (2006)
  • Author(s): Yoshihito Oshita
  • Organizer: Recent advances in Free Boundary Problemsand related topics
  • Place of Presentation: Levico, Italy
  • Year and Date: 2006-09-15
• [Presentation] Singular limit problem for some elliptic systems (2006)
  • Author(s): Yoshihito Oshita
  • Organizer: 変分問題とその周辺
  • Place of Presentation: 京都
  • Year and Date: 2006-06-21
• [Presentation] 楕円型方程式系の特異極限問題 (2006)
  • Author(s): 大下承民
  • Organizer: 広島数理解析セミナー第98回
  • Place of Presentation: 東広島
  • Year and Date: 2006-05-19