ANALYSIS OF SYSTEMS OF DIFFERENTIAL EQUATIONS HAVING SEVERAL NONLOCAL TERMS AND APPLICATIONS

具有多项非局部项的微分方程组的分析及应用

• 批准号: 15540172
• 负责人: KATO Nobuyuki
• 金额: $ 1.66万
• 依托单位: SHIMANE UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540172/
• 关键词: nonlocal; population dynamics; size structured; harvesting; time dependent; transport equation; muscle contraction; 非局所非線形成長率

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.

首先，我们研究了人口规模结构模型，其中增长率、死亡率和生育率取决于人口规模和总人口权重。我们得到了解的存在、表示和唯一性。利用Schauder不动点定理，我们得到了一般模型解的存在性。为了独特性，我们对死亡率和生育率施加了一些更强的条件。不幸的是，目前还不知道是否可以消除更强的条件。这一结果发表在《J.Math.Anal.Appl.》杂志上。接下来，我们研究了一个一般的大小结构种群动力学的依赖于时间的模型，其中增长率取决于大小和时间。我们得到了解的存在性、正性和唯一性。时间依赖模型的研究是考虑非线性收获问题所必需的。事实上，我们将结果应用于一个大小结构种群模型的非线性收获问题。我们的模型具有只依赖于时间的收获率，但增长率依赖于大小和时间，生育率依赖于加权的总人口.我们在2004年在佛罗里达举行的国际会议上介绍了这一结果.进一步，我们发展了由多值函数描述的具有非局部项的非线性传输方程的理论，并将其应用于肌肉收缩的非线性四状态模型.在此，我们不仅得到了解的存在唯一性结果，而且得到了解的支撑性和有界性的结果.研究结果将发表在《高级数学科学分析》杂志上。

项目成果

A system of nonlinear nonlocal transport equations related to muscle contraction mechanism

与肌肉收缩机制相关的非线性非局部传输方程组

• 期刊: Adv.Math.Sci.Appl. (発表予定)
• 作者: T.Ichinose;D.Fan;G.G.Gundersen;佐藤 秀一;G.G.Gundersen;Y.Kanjin;Y.Kanjin;T.Ichinose;N.Kato;N.Kato
• 通讯作者: N.Kato

H.Aikawa: "Positive harmonic functions of finite order in a Denjoy type domain"Proc.Amer.Math.Soc.. 131. 3873-3881 (2003)

H.Aikawa：“Denjoy 型域中有限阶的正调和函数”Proc.Amer.Math.Soc.. 131. 3873-3881 (2003)

A general model of size-dependent population dynamics with nonlinear growth rate

• DOI: 10.1016/j.jmaa.2004.05.004
• 发表时间: 2004-09
• 期刊: Journal of Mathematical Analysis and Applications
• 影响因子: 1.3
• 作者: N. Kato

T.Furumochi, S.Murakami, Y.Nagabuchi: "Stabilities in Volterra difference equations on a Banach space"Fields Institute Communications. (to appear).

T.Furumochi、S.Murakami、Y.Nagabuchi：“Banach 空间上 Volterra 差分方程的稳定性”Fields Institute Communications。

S.Machihara, K.Nakanishi, T.Ozawa: "Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation"Revista Matematica Iberoamericana. 19. 179-194 (2003)

S.Machihara、K.Nakanishi、T.Ozawa：“非线性狄拉克方程的小全局解和非相对论极限”Revista Matematica Iberoamericana。