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Titlebook: Dynamical Systems and Evolution Equations; Theory and Applicati J. A. Walker Book 1980 Springer Science+Business Media New York 1980 Area.F

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发表于 2025-3-21 18:44:48 | 显示全部楼层 |阅读模式
书目名称Dynamical Systems and Evolution Equations
副标题Theory and Applicati
编辑J. A. Walker
视频video
丛书名称Mathematical Concepts and Methods in Science and Engineering
图书封面Titlebook: Dynamical Systems and Evolution Equations; Theory and Applicati J. A. Walker Book 1980 Springer Science+Business Media New York 1980 Area.F
描述This book grew out of a nine-month course first given during 1976-77 in the Division of Engineering Mechanics, University of Texas (Austin), and repeated during 1977-78 in the Department of Engineering Sciences and Applied Mathematics, Northwestern University. Most of the students were in their second year of graduate study, and all were familiar with Fourier series, Lebesgue integration, Hilbert space, and ordinary differential equa­ tions in finite-dimensional space. This book is primarily an exposition of certain methods of topological dynamics that have been found to be very useful in the analysis of physical systems but appear to be well known only to specialists. The purpose of the book is twofold: to present the material in such a way that the applications-oriented reader will be encouraged to apply these methods in the study of those physical systems of personal interest, and to make the coverage sufficient to render the current research literature intelligible, preparing the more mathematically inclined reader for research in this particular area of applied mathematics. We present only that portion of the theory which seems most useful in applications to physical systems.
出版日期Book 1980
关键词Area; Finite; Hilbert space; Lebesgue integration; Mathematica; behavior; control; dynamical systems; equati
版次1
doihttps://doi.org/10.1007/978-1-4684-1036-5
isbn_softcover978-1-4684-1038-9
isbn_ebook978-1-4684-1036-5
copyrightSpringer Science+Business Media New York 1980
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发表于 2025-3-21 23:19:45 | 显示全部楼层
Preliminaries for Abstract Evolution Equations, space χ = ℛ.,.We now wish to consider this type of equation with χ denoting some type of abstract space. Roughly speaking, we hope to describe the evolution in time of almost . physical system by an evolution equation similar to (1); we hope to obtain much information about the time behavior of the
发表于 2025-3-22 01:01:53 | 显示全部楼层
Abstract Dynamical Systems and Evolution Equations,ith the physics of the system but are made for the convenience of the modeler; that is, they are made so that the formal equation “makes sense.” To a mathematician not interested in applications, such artificial assumptions are as good as any others, and their occasionally disruptive effect on exist
发表于 2025-3-22 07:02:09 | 显示全部楼层
Some Topological Dynamics,ping .(.).: ℛ. → χ is the motion corresponding to the initial state . ∈ χ, .. ∈ χ is an equilibrium if .(.).. = .. for all . ∈ ℛ., and a set δ ⊂ χ is positive invariant if . ∈ δ implies that .(.). ∈ δ for all . ∈ ℛ.. We define the set γ(.) ≡ ⋃. ≥..(.). to be the . corresponding to the initial state
发表于 2025-3-22 10:36:34 | 显示全部楼层
Applications and Special Topics, case) or processes (nonautonomous case). It follows that the techniques described in Chapters III and IV can be very useful in analyzing the time behavior of autonomous physical systems; in Sections III.6 and IV.6 we also mentioned that these techniques admit nonautonomous extensions. With increasi
发表于 2025-3-22 16:04:34 | 显示全部楼层
Epilog, to be able to use this equation to predict the future for that physical system, given initial data about the “initial state” of the system, as well as data about the “future” of all external agents that affect the system. We believe that any physical system . a future, which is necessarily of infin
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发表于 2025-3-23 03:19:32 | 显示全部楼层
Führer und Geführte. Werner Koflers Film ping .(.).: ℛ. → χ is the motion corresponding to the initial state . ∈ χ, .. ∈ χ is an equilibrium if .(.).. = .. for all . ∈ ℛ., and a set δ ⊂ χ is positive invariant if . ∈ δ implies that .(.). ∈ δ for all . ∈ ℛ.. We define the set γ(.) ≡ ⋃. ≥..(.). to be the . corresponding to the initial state
发表于 2025-3-23 05:55:42 | 显示全部楼层
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