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: Analysis and computation of multiple unstable solutions to nonlinear elliptic systems
  name:
    name part: Chen, Xianjin.
    role:
      role term: creator
  name:
    name part: Zhou, Jianxin
    role:
      role term: thesis advisor.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: txu
    date issued: 2010
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: remote
    extent: 1 online resource.
  abstract: We study computational theory and methods for finding multiple unstable solutions (corresponding to saddle points) to three types of nonlinear variational elliptic systems: cooperative, noncooperative, and Hamiltonian. We first propose a new Lorthogonal selection in a product Hilbert space so that a solution manifold can be defined. Then, we establish, respectively, a local characterization for saddle points of finite Morse index and of infinite Morse index. Based on these characterizations, two methods, called the local min-orthogonal method and the local min-max-orthogonal method, are developed and applied to solve those three types of elliptic systems for multiple solutions. Under suitable assumptions, a subsequence convergence result is established for each method. Numerical experiments for different types of model problems are carried out, showing that both methods are very reliable and efficient in computing coexisting saddle points or saddle points of infinite Morse index. We also analyze the instability of saddle points in both single and product Hilbert spaces. In particular, we establish several estimates of the Morse index of both coexisting and non-coexisting saddle points via the local min-orthogonal method developed and propose a local instability index to measure the local instability of both degenerate and nondegenerate saddle points. Finally, we suggest two extensions of an L-orthogonal selection for future research so that multiple solutions to more general elliptic systems such as nonvariational elliptic systems may also be found in a stable way.
  note: by Xianjin Chen.
  note: "Major Subject: Mathematics"
  note: Title from author supplied metadata (automated record created 2010-03-12 12:08:51).
  note: Electronic resource.
  note: Doctor of Philosophy Texas A&M University 2008 http://hdl.handle.net/1969.1/ETD-TAMU-2990
  note: Includes bibliographical references.
  note: Text (Dissertation)
  subject:
    topic: Major mathematics
  subject:
    topic: Saddle point computation
  subject:
    topic: Min-orthogonal method
  subject:
    topic: Min-max-orthogonal method
  subject:
    topic: Multiple solutions
  subject:
    topic: Variational elliptic systems
  identifier: http://hdl.handle.net/1969.1/ETD-TAMU-2990
  record info:
    record content source: TXA
    record creation date: 100427
    record change date: 20151201120137.0
    record identifier: in00002578019