CIASSIFICATIONS OF FONC TIONAL DIFFERENTIAL EQUATIONS BY PROCESSES

按过程分类的函数微分方程

• 批准号: 09640156
• 负责人: HINO Yoshiyuki
• 金额: $ 1.98万
• 依托单位: CHIBA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640156/
• 关键词: process; functional differential Egs; skew produt flow; stability; almost periodic function; 極限方程式

Let B = B((-*, 0] ; X), where X is a complete metric space. Consider functional differential equations with infinite delaydu/dt = AIOTA(t) + L(t, IOTA_t),where A is an infinitesimal generator of a compact semigroup of bounded lineat operators and IOTA_t is an element of B defined by IOTA_t (s) =IOTA_t (t + s), s epsilon (-*, 0).This phase space has two types, that is, one is a uniform fading memory space and the other is a fading memory space. Furthermore, if we consider an evolution equations which is a genaralization of partial differential equations, above equation must be considered a functional partial differential equation with infinite delay. In this report, we have the followings :(i) Stability theoris are characterized by processes. We have a new concept of process which is a generalization of processes and we called it a quasi-process.(ii) Nonlinear oscillations are characterized by processes. In particular, the existence of an almost periodic integral of almost periodic processes is given.Inaba has given an example of a flow on a non-compact surface without minimal set. This result has given important informations to solve a problem (ii).

设 B = B((-*, 0] ; X)，其中 X 是完全度量空间。考虑具有无限延迟的函数微分方程 du/dt = AIOTA(t) + L(t, IOTA_t)，其中 A 是有界线性算子的紧半群的无穷小生成元，IOTA_t 是由 IOTA_t (s) =IOTA_t (t + 定义的 B 的元素 s), s epsilon(-*, 0)。该相空间有两种类型，一种是均匀衰落存储空间，另一种是衰落存储空间。此外，如果我们考虑一个偏微分方程的推广方程，则上述方程必须被视为具有无限延迟的函数偏微分方程。在本报告中，我们有以下内容：(i) 稳定性理论的特点是 流程。我们有一个新的过程概念，它是过程的概括，我们称之为准过程。（ii）非线性振荡以过程为特征。特别是，给出了几乎周期过程的几乎周期积分的存在性。Inaba 给出了一个没有最小集的非紧表面上的流的例子。该结果为解决问题(ii)提供了重要信息。

项目成果

日野 義之・村上 悟: "Almost periodic processes and the existence of almost periodic solutions" Electric Journal of Quslifatiue Theory of Differential Equations. 1. 1-19 (1998)

Yoshiyuki Hino 和 Satoru Murakami：“几乎周期过程和几乎周期解的存在”《Electric Journal of Quslifatiue 微分方程理论》1. 1-19 (1998)。

HINO Yoshiyuki and MURAKAMI Satoru: "A generalization of processes an stabilities in abstract functional differential equations" Functialaj Ekvacioj. 41. 235-255 (1998)

HINO Yoshiyuki 和 MURAKAMI Satoru：“抽象函数微分方程中过程和稳定性的概括”Functialaj Ekvacioj。

Yoshiyuki Hino & Satoru Murakami: "Skew product flows of quasi-prosesses and stahilitces" The fields inslitute communications volume. (to appear).

日野由之

稲葉 尚志: "An example of a flow on a non-compact surface without minimal set" Ergod.th. & Dynamical Systems. 19巻1-3号. 1-3 (1999)

Takashi Inaba：“无最小集的非紧致表面上的流动示例”Ergod.th 和 Dynamical Systems，第 19 卷，第 1-3 期。

岡田 靖則他: "A remark on 2-microhyperbolicify" Proc. Japan Academy. 74. 39-42 (1998)

Yasunori Okada 等人：“关于 2-microhyperbolicify 的评论”Proc. 74. 39-42 (1998)