权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Theory and Applications of Evolution Equations with Nonlocal Conditions

非局部条件演化方程的理论与应用

基本信息

批准号：
10640172
负责人：
KATO Nobuyuki
金额：
$ 2.18万
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：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640172/
关键词：
nonlocal evolution equation muscle contraction population dynamics size-dependent 固体数変動

项目摘要

We have investigated two different types of evolution equations, focusing on the common key word "nonlocal conditions".[Muscle contraction models]The muscle contraction is a consequence of relative sliding between the thick filament (Myosin) and the thin filament (Actin).This sliding occurs when the so-called cross-bridges attach Myosin to Actins, and act as spring.The Muscle contraction model describes the temporal variation of the density of the attached cross-bridges.Since the contraction speed is dependent on the number of the attached cross-bridges, a nonlocal term appears in the model.In this research, we have considered transport equations of hyperbolic type and transport-diffusion equations of parabolic type.We obtained the existence and uniqueness results with some general setting allowing the attaching and detaching of the cross-bridges being nonlinear.[Population dynamics]The population model depending on the individuals size and time has been investigated as a natural model describing the population of plants in forests or plantations.The birth law includes a nonlocal term.We obtained some results concerning the existence of positive solutions and blow up and global existence of the solution to a general model.I had a talk on these results in the international conference held at Newport Beach, USA in 1998.Also, we have shown the continuous dependence on the birth and aging functions as well as initial data.Besides, we have investigated the model having the nonlinear growth rate and obtained the existence result.I had a talk on this in the international conference held at Berlin, Germany in 1999.

我们研究了两种不同类型的发展方程，重点是共同的关键词“非局部条件”。[肌肉收缩模型]肌肉收缩是粗丝（肌球蛋白）和细丝（肌动蛋白）之间相对滑动的结果。这种滑动发生在所谓的横桥将肌球蛋白连接到肌动蛋白上并起弹簧作用时。肌肉收缩模型描述了连接的横桥密度的时间变化。由于收缩速度取决于连接的横桥的数量，本文考虑了双曲型迁移方程和抛物型迁移扩散方程，在一定的一般条件下，得到了非线性跨桥连接和分离的解的存在唯一性结果. [种群动力学]作为描述森林或人工林中植物种群的自然模型，研究了依赖于个体大小和时间的种群模型。出生律中包含一个非局部项。我们得到了关于一般模型正解的存在性和解的爆破和整体存在性的一些结果。我在纽波特海滩举行的国际会议上发表了这些结果。1998年在美国的一次会议上，我们证明了该模型对出生函数、年龄函数以及初始数据的连续依赖性，并研究了具有非线性增长率的模型，得到了该模型的存在性结果，我在1999年德国柏林国际会议上作了报告。