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Titlebook: Semigroup Methods for Evolution Equations on Networks; Delio Mugnolo Book 2014 Springer International Publishing Switzerland 2014 Mathemat

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发表于 2025-3-21 17:31:22 | 显示全部楼层 |阅读模式
书目名称Semigroup Methods for Evolution Equations on Networks
编辑Delio Mugnolo
视频video
概述Course-based and self-contained presentation.Suitable as graduate textbook or self-study guide.Combines classical results on hyperbolic and parabolic equations on networks with operator semigroup appr
丛书名称Understanding Complex Systems
图书封面Titlebook: Semigroup Methods for Evolution Equations on Networks;  Delio Mugnolo Book 2014 Springer International Publishing Switzerland 2014 Mathemat
描述.This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations..This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has beendevoted to elliptic equations and related spectral problems. Moreover, for tackling the most general settings - e.g. encoded in the transmission conditions in the network nodes - one classical and elegant too
出版日期Book 2014
关键词Mathematical Modeling of Neuronal Networks; Operator Semi-groups and Graph Theory; Parabolic Evolution
版次1
doihttps://doi.org/10.1007/978-3-319-04621-1
isbn_softcover978-3-319-37474-1
isbn_ebook978-3-319-04621-1Series ISSN 1860-0832 Series E-ISSN 1860-0840
issn_series 1860-0832
copyrightSpringer International Publishing Switzerland 2014
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Function Spaces on Networks,er we introduce some relevant spaces of functions on networks. We assume the theory of Lebesgue spaces to be known to the reader, whilst the fundamental aspects of the theory of Sobolev spaces are summarized in the Appendix B. Throughout this chapter
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Symmetry Properties,er on or on the metric graph over it. We will use the word “symmetry” in a rather broad sense, to mean different notions of structural regularity of graphs of the Laplacian on..The common thread in our discussion is the search for reductions of an equation. By this we mean the possibility of decompo
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1860-0832 parabolic equations on networks with operator semigroup appr.This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramif
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And Now Something Completely Different: A Crash Course in Cortical Modeling,n phenomena so ubiquitous in nature? An answer is not known—or perhaps this question is ill-posed all-together. Still, we feel that we owe the reader some convincing examples of real-life emergence of diffusion-type equations as well as of differential equations in networks.
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