2011 Fiscal Year Final Research Report
Mathematical Analysis for competition between species in heterogeneous environment
| Project/Area Number |
20540109
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Kanazawa University (2011)
The University of Electro-Communications (2008-2010) |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
MATANO Hiroshi 東京大学, 大学院・数理科学研究科, 教授 (40126165)
NAKAMURA Toshiko (OGIWARA Toshiko) 城西大学, 理学部, 准教授 (70316678)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 反応拡散系 / 進行波解 / 均質化極限 / 界面方程式 / 数理生態学 |
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| Research Abstract |
In this research project, for the mathematical study of competition between biological species in heterogeneous environment, we investigated the effect of spatial inhomogeneity on the propagating speed of traveling waves of 2-species Lotka-Volterra competition-diffusion systems and their singular limit equations. Among other things, we obtained sharp estimates of the average propagation speed of traveling waves in spatially periodic environment, showed the existence and the asymptotic stability of recurrent traveling waves and established conditions for the well-definedness of the average speed of the recurrent traveling wave. We also considered the homogenization problem and determined the homogenization limit of the average speed and the limit profile of the traveling waves
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