bile-acids 发表于 2025-3-21 18:44:48
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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 theGRAZE 发表于 2025-3-22 01:01:53
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退潮 发表于 2025-3-22 07:02:09
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和平 发表于 2025-3-22 10:36:34
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范围广 发表于 2025-3-22 16:04:34
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范围广 发表于 2025-3-22 18:27:04
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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 stateAV-node 发表于 2025-3-23 05:55:42
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