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: Self-dual Partial Differential Systems and Their Variational Principles
  name:
    name part: Ghoussoub, Nassif.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2009
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 354 p. online resource.
  abstract: Based on recent research by the author and his graduate students, this text describes novel variational formulations and resolutions of a large class of partial differential equations and evolutions, many of which are not amenable to the methods of the classical calculus of variations. While it contains many new results, the general and unifying framework of the approach, its versatility in solving a disparate set of equations, and its reliance on basic functional analytic principles, makes it suitable for an intermediate level graduate course. The applications, however, require a fair knowledge of classical analysis and PDEs which is needed to make judicious choices of function spaces where the self-dual variational principles need to be applied. It is the author's hope that this material will become standard for all graduate students interested in convexity methods for PDEs. Nassif Ghoussoub is a Distinguished University Professor at the University of British Columbia. He was editor-in-chief of the Canadian Journal of Mathematics for the period 1993-2003, and has served on the editorial board of various international journals. He is the founding director of the Pacific Institute for the Mathematical Sciences (PIMS), and a co-founder of the MITACS Network of Centres of Excellence. He is also the founder and scientific director of the Banff International Research Station (BIRS). He is the recipient of many awards, including the Coxeter-James, and the Jeffrey-Williams prizes. He was elected Fellow of the Royal Society of Canada in 1993, and was the recipient of a Doctorat Honoris Causa from the Universite Paris-Dauphine in 2004.
  table of contents: Convex Analysis on Phase Space -- Legendre-Fenchel Duality on Phase Space -- Self-dual Lagrangians on Phase Space -- Skew-Adjoint Operators and Self-dual Lagrangians -- Self-dual Vector Fields and Their Calculus -- Completely Self-Dual Systems and their Lagrangians -- Variational Principles for Completely Self-dual Functionals -- Semigroups of Contractions Associated to Self-dual Lagrangians -- Iteration of Self-dual Lagrangians and Multiparameter Evolutions -- Direct Sum of Completely Self-dual Functionals -- Semilinear Evolution Equations with Self-dual Boundary Conditions -- Self-Dual Systems and their Antisymmetric Hamiltonians -- The Class of Antisymmetric Hamiltonians -- Variational Principles for Self-dual Functionals and First Applications -- The Role of the Co-Hamiltonian in Self-dual Variational Problems -- Direct Sum of Self-dual Functionals and Hamiltonian Systems -- Superposition of Interacting Self-dual Functionals -- Perturbations of Self-Dual Systems -- Hamiltonian Systems of Partial Differential Equations -- The Self-dual Palais-Smale Condition for Noncoercive Functionals -- Navier-Stokes and other Self-dual Nonlinear Evolutions.
  note: by Nassif Ghoussoub.
  subject:
    topic: Mathematics
  subject:
    topic: Information technology
  subject:
    topic: Business
    topic: Data processing
  subject:
    topic: Functional analysis
  subject:
    topic: Partial differential equations
  subject:
    topic: Mathematics
  subject:
    topic: Functional Analysis
  subject:
    topic: Partial Differential Equations
  subject:
    topic: IT in Business
  classification: QA319-329.9
  classification: 515.7
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9780387848976
  identifier: http://dx.doi.org/10.1007/978-0-387-84897-6
  record info:
    record creation date: 100301
    record change date: 20151204154958.0
    record identifier: 978-0-387-84897-6