Semigroup Methods for Evolution Equations ...

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Sprache: Englisch

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Beschreibung

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 tool is that of operator semigroups. This book is simultaneously a very concise introduction to this theory and a handbook on its applications to differential equations on networks.
With a more interdisciplinary readership in mind, full proofs of mathematical statements have been frequently omitted in favor of keeping the text as concise, fluid and self-contained as possible. In addition, a brief chapter devoted to the field of neurodynamics of the brain cortex provides a concrete link to ongoing applied research.

Zusammenfassung

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 approaches

Inhaltsverzeichnis

Introduction.- Operators on Networks.- Function Spaces on Networks.- Operator Semigroups.- And Now Something Completely Different: A Crash Course in Cortical Modeling.- Sequilinear Froms and Analytic Semigroups.- Evolution Equations Associated With Self-adjoint Operators.- Symmetry Properties.- Index.

Erscheinungsjahr:	2016
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Understanding Complex Systems
Inhalt:	xv 286 S. 32 s/w Illustr. 1 farbige Illustr. 286 p. 33 illus. 1 illus. in color.
ISBN-13:	9783319374741
ISBN-10:	3319374745
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Mugnolo, Delio
Auflage:	Softcover reprint of the original 1st ed. 2014
Hersteller:	Springer International Publishing Springer International Publishing AG Understanding Complex Systems
Maße:	235 x 155 x 17 mm
Von/Mit:	Delio Mugnolo
Erscheinungsdatum:	23.08.2016
Gewicht:	0,464 kg

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