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:
    non sort: The
    title: Convergence Problem for Dissipative Autonomous Systems
    sub title: Classical Methods and Recent Advances
  name:
    name part: Haraux, Alain.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Jendoubi, Mohamed Ali.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2015
    edition: 1st ed. 2015.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 142 p. 1 illus. in color. online resource.
  abstract: The book investigates classical and more recent methods of study for the asymptotic behavior of dissipative continuous dynamical systems with applications to ordinary and partial differential equations, the main question being convergence (or not) of the solutions to an equilibrium. After reviewing the basic concepts of topological dynamics and the definition of gradient-like systems on a metric space, the authors present a comprehensive exposition of stability theory relying on the so-called linearization method. For the convergence problem itself, when the set of equilibria is infinite, the only general results that do not require very special features of the non-linearities are presently consequences of a gradient inequality discovered by S. Lojasiewicz. The application of this inequality jointly with the so-called Liapunov-Schmidt reduction requires a rigorous exposition of Semi-Fredholm operator theory and the theory of real analytic maps on infinite dimensional Banach spaces, which cannot be found anywhere in a readily applicable form. The applications covered in this short text are the simplest, but more complicated cases are mentioned in the final chapter, together with references to the corresponding specialized papers.
  table of contents: 1 Introduction -- 2 Some basic tools -- 3 Background results on Evolution Equations.- 4 Uniformly damped linear semi-groups.- 5 Generalities on dynamical systems.- 6 The linearization method.- 7 Gradient-like systems.- 8 Liapunov’s second method - invariance principle.- 9 Some basic examples.- 10 The convergence problem in finite dimensions -- 11 The infinite dimensional case -- 12 Variants and additional results.
  note: by Alain Haraux, Mohamed Ali Jendoubi.
  subject:
    topic: Mathematics
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Functional analysis
  subject:
    topic: Operator theory
  subject:
    topic: Differential equations
  subject:
    topic: Partial differential equations
  subject:
    topic: Mathematics
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Functional Analysis
  subject:
    topic: Operator Theory
  subject:
    topic: Ordinary Differential Equations
  classification: QA313
  classification: 515.39
  classification: 515.48
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SpringerBriefs in Mathematics
  identifier: 9783319234076
  identifier: http://dx.doi.org/10.1007/978-3-319-23407-6
  record info:
    record creation date: 150905
    record change date: 20151124031339.0
    record identifier: 978-3-319-23407-6