ANALYSIS OF SYSTEMS OF DIFFERENTIAL EQUATIONS HAVING SEVERAL NONLOCAL TERMS AND APPLICATIONS
| Project/Area Number | 15540172 |
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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 |
Basic analysis
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| Research Institution | SHIMANE UNIVERSITY |
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Principal Investigator |
KATO Nobuyuki Shimane University, Dept.Math, Associate Professor, 総合理工学部, 助教授 (40177423)
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| Co-Investigator(Kenkyū-buntansha) |
FURUMOCHI Tetsuo Shimane University, Dept.Math, Professor, 総合理工学部, 教授 (40039128)
AIKAWA Hiroaki Shimane University, Dept.Math, Professor, 総合理工学部, 教授 (20137889)
SUGIE Jitsuro Shimane University, Dept.Math, Professor, 総合理工学部, 教授 (40196720)
MACHIHARA Shuji Shimane University, Dept.Math, Research Associate, 総合理工学部, 助手 (20346373)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed(Fiscal Year 2004)
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| Budget Amount *help |
¥2,600,000 (Direct Cost : ¥2,600,000)
Fiscal Year 2004 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 2003 : ¥1,500,000 (Direct Cost : ¥1,500,000)
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| Keywords | nonlocal / population dynamics / size structured / harvesting / time dependent / transport equation / muscle contraction / 非局所非線形成長率 |
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| Research Abstract |
First, we have investigated size structured population models where the growth rate, the mortality rate and the fertility rate depend on size and total population weighted differently each other. We obtained the existence, the representation, and the uniqueness of solutions. By using Schauder's fixed point theorem, we obtained the existence of solutions in a general model. For the uniqueness, we imposed some stronger conditions on the mortality rate and the fertility rate. Unfortunately, it is not known whether the stronger conditions can be removed or not. The results are published in the journal, J.Math.Anal.Appl.
Next, we have investigated a general time-dependent model of size structured population dynamics, where the growth rate depends on the size and time. We obtained the existence, positivity, and the uniqueness of solutions. The study of the time dependent model is needed to consider nonlinear harvesting problems.
In fact, we applied the results to a nonlinear harvesting problem of size structured population models. Our model has the harvesting rate depending only on time, but the growth rate depends on the size and time and the fertility rate depends on the weighted total population.
We gave a presentation about this result at the international conference held at Florida in 2004.
Further, we have developed the theory of nonlinear transport equations with nonlocal terms prescribed by a multi-valued function and applied the results to nonlinear four state models of muscle contraction.
Here, we obtained not only the existence and uniqueness results, but also the results of the support and the boundedness of the solution. The results will be published in the journal, Adv.Math.Sci.Anal.
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Report
(3results)
Research Products
(8results)
