2013 Fiscal Year Final Research Report
On a study on dynamics of localized pattern for a bistable reaction diffusion equations with a heterogeneous environment
| Project/Area Number |
23740137
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Numazu National College of Technology |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2012
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| Keywords | 反応拡散方程式 / 自由境界問題 / 偏微分方程式 / 放物型方程式 |
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| Research Abstract |
In this research, we study free boundary problems for nonlinear diffusions equations. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundaries representing the expanding fronts. If the nonlinearity is monostable, bistable, or combustion type, Professor Du and Professor Lou obtained a rather complete description of the long-time dynamical behavior of the problem and revealed sharp transition phenomena between so called "spreading" and "vanishing". They also determined the asymptotic spreading speed of the fronts by using of "semi-waves" when spreading happens. In this research we we give a much sharper estimate for the spreading speed of the fronts than that in the work of Du and Lou, and we describe how the solution approaches the semi-wave when spreading happens. I obtained these results for (1)1 dimensional problem, (2)higher dimensional problem with radially symmetric setting and (3)1 dimensional advection-diffusion problem.
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Research Products
(14 results)
