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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.
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.
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
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, Medizin, Naturwissenschaften, Technik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
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 |
Einband: | Kartoniert / Broschiert |
Autor: | Mugnolo, Delio |
Auflage: | Softcover reprint of the original 1st edition 2014 |
Hersteller: |
Springer Nature Switzerland
Springer International Publishing |
Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
Maße: | 235 x 155 x 17 mm |
Von/Mit: | Delio Mugnolo |
Erscheinungsdatum: | 23.08.2016 |
Gewicht: | 0,464 kg |
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
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, Medizin, Naturwissenschaften, Technik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
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 |
Einband: | Kartoniert / Broschiert |
Autor: | Mugnolo, Delio |
Auflage: | Softcover reprint of the original 1st edition 2014 |
Hersteller: |
Springer Nature Switzerland
Springer International Publishing |
Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
Maße: | 235 x 155 x 17 mm |
Von/Mit: | Delio Mugnolo |
Erscheinungsdatum: | 23.08.2016 |
Gewicht: | 0,464 kg |