2002 Fiscal Year Final Research Report Summary
Development of reaction-diffusion systems - Studies of singular limit methods -
| Project/Area Number |
12304006
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | HIROSHIMA UNIVERSITY |
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Principal Investigator |
MIMURA Masayasu Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (50068128)
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| Co-Investigator(Kenkyū-buntansha) |
YANAGIDA Eiji Tohoku University Graduate School of Sciences, Professor, 大学院・理学研究科, 教授 (80174548)
SAKAMOTO Kunimochi Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40243547)
OHTA Takao Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (50127990)
IKEDA Hideo Toyama University, Faculty of Sciences, Professor, 理学部, 教授 (60115128)
MORITA Yoshihisa Ryukoku Univ., Faculty of Science and Technolgy, Professor, 理工学部, 教授 (10192783)
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| Project Period (FY) |
2000 – 2002
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| Keywords | Singular limit methods / Interfacial dynamics / Singular perturbation method / Blow up problem / Traveling wave solutions / Equations of curvature / Chemotaxis equations / Center manifold theory |
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| Research Abstract |
Reaction-diffusion systems have been encountered in many fields of natural sciences. In this project, we develop singular limit procedures and comtempolarily numerical methods in order to investigate dynamics of patterns, forms, interfaces and singularities in such systems. In the below, we show our results obtained in this project:
(1) Derivation of a free boundary problem from competition-diffusion systems by using singular limit procedures
(2) Qualitative study of spiky solutions in biological systems by singular limit procedures.
(3) Stability analysis of skew-gradient reaction-diffusion systems.
(4) Interaction of traveling pulses and spots by using dynamical system theory
(5) Traveling wave solutions of reaction diffusion systems by using singular perturbation methods
(6) analysis of motion of mean curvatures in higher dimensional spaces.
(7) Analysis of aggregating patterns in diffusion-chemotaxis systems
(8) Numerical simulations of complex spatio-temporal patterns in reaction-diffusion systems
(9) Development of adoptive FEM methods to reaction-diffusion systems
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