rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Semigroup Methods for Evolution Equations on Networks
  name:
    name part: Mugnolo, Delio.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XV, 286 p. 33 illus., 1 illus. in color. online resource.
  abstract: 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 been devoted 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.
  table of contents: 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.
  note: by Delio Mugnolo.
  subject:
    topic: Physics
  subject:
    topic: System theory
  subject:
    topic: Graph theory
  subject:
    topic: Statistical physics
  subject:
    topic: Complexity, Computational
  subject:
    topic: Physics
  subject:
    topic: Complex Networks
  subject:
    topic: Graph Theory
  subject:
    topic: Nonlinear Dynamics
  subject:
    topic: Complex Systems
  subject:
    topic: Complexity
  classification: QC1-QC999
  classification: 621
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Understanding Complex Systems
  identifier: 9783319046211
  identifier: http://dx.doi.org/10.1007/978-3-319-04621-1
  record info:
    record creation date: 140521
    record change date: 20151030061118.0
    record identifier: 978-3-319-04621-1