2009 Fiscal Year Final Research Report
New development in the theory of reaction-diffusion system approximation
| Project/Area Number |
19740046
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Toyama |
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Principal Investigator |
MURAKAWA Hideki University of Toyama, 大学院・理工学研究部(理学), 助教 (40432116)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 非線形拡散問題 / 退化放物型問題 / 非線形交差拡散系 / 反応拡散系 / 数値解法ステファン問題 / 多孔質媒体流方程式 |
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| Research Abstract |
We dealt with nonlinear diffusion problems arising in a large number of important scientific and industrial contexts. The difficulties arise from the nonlinearity of the diffusion and the problem is how to handle the nonlinearity of the diffusion. In this study, we proved that the solutions of the nonlinear diffusion problems can be approximated by those of semilinear reaction-diffusion systems which include only simple reactions and linear diffusions. This indicates that the mechanism of nonlinear diffusion might be captured by reaction-diffusion interaction. Resolving semilinear problems is typically easier than dealing with nonlinear problems. Therefore, the theory of reaction-diffusion system approximation is expected to reveal effective approaches to the study of nonlinear problems.
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