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System of nonlocal nonlinear differential equations and applications

非局部非线性微分方程组及其应用

基本信息

批准号：
13640174
负责人：
KATO Nobuyuki
金额：
$ 1.92万
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：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

项目摘要

First, we have investigated the population models with growth rate depending on size and time. Continuous dependence of solution on all given data is obtained. For the dependency on initial values, aging functions and birth functions, it is shown relatively simply, but the dependency on growth rate includes an essentially difficult problem. The way of solving equation is so-called the characteristic method and the characteristic curves are determined by the growth rate, and so when the growth rate is perturbed, the characteristic curves themselves change. The results here are important as the stability of equation, and at the same time, they can be used to investigate the models with nonlinear growth rate.Next, we have investigated the size-dependent population models with growth rate depending on size and the total population. Originally, the models come from describing the population dynamics of plants in forests or plantations. We obtained the existence and uniqueness results for more general models and we gave a presentation about this result at the international conference held at Hong Kong in 2002.Muscle contraction is a consequence of relative sliding between tha thick filament called myosin and the thin filament called actin. This sliding occurs when the so-called cross-bridges attach myosin to actin and act as spring. The muscle contraction models describe the temporal variation of the density of the attached cross-bridges. In this research, we have considered a system of hyperbolic transport equations. Our model contains the so-called four state models in which there are two state of attached and detached cross-bridges respectively.

首先，我们研究了增长率随规模和时间变化的人口模型。得到了解对所有给定数据的连续依赖。对于初始值、老化函数和出生函数的依赖关系，表现得相对简单，但对增长率的依赖关系包含了一个本质上困难的问题。求解方程的方法称为特征法，特征曲线是由生长速率决定的，当生长速率受到扰动时，特征曲线本身也会发生变化。所得结果对方程的稳定性具有重要意义，同时也可用于研究具有非线性增长率的模型。其次，我们研究了人口规模依赖模型，增长率取决于人口规模和总人口。最初，这些模型来自于描述森林或种植园中植物的种群动态。我们得到了更一般模型的存在唯一性结果，并于2002年在香港举行的国际会议上发表了这一结果。肌肉收缩是肌凝蛋白（myosin）和肌动蛋白（actin）之间相对滑动的结果。当所谓的交叉桥将肌凝蛋白连接到肌动蛋白上并起到弹簧的作用时，这种滑动就发生了。肌肉收缩模型描述了连接的交叉桥密度的时间变化。在这项研究中，我们考虑了一个双曲输运方程系统。我们的模型包含了所谓的四状态模型，其中分别有连接和分离两种状态的桥梁。