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    Полное описание

    Rabinowitz, P. H. Extensions of Moser–Bangert Theory : locally Minimal Solutions / by Paul H. Rabinowitz, Edward W. Stredulinsky. - Boston : Birkhäuser, 2011. - on-line. - (Progress in Nonlinear Differential Equations and Their Applications ; vol. 81). - URL: http://dx.doi.org/10.1007/978-0-8176-8117-3. - Загл. с экрана. - ISBN 978-0-8176-8117-3. - Текст : электронный.
    Содержание:
    1 Introduction -- Part I: Basic Solutions -- 2 Function Spaces and the First Renormalized Functional -- 3 The Simplest Heteroclinics -- 4 Heteroclinics in x1 and x2 -- 5 More Basic Solutions -- Part II: Shadowing Results -- 6 The Simplest Cases -- 7 The Proof of Theorem 6.8 -- 8 k-Transition Solutions for k > 2 -- 9 Monotone 2-Transition Solutions -- 10 Monotone Multitransition Solutions -- 11 A Mixed Case -- Part III: Solutions of (PDE) Defined on R

    ГРНТИ УДК
    27.39.25517.938

    Рубрики:
    mathematics
    food -- Biotechnology.
    mathematical analysis
    analysis (Mathematics)
    dynamics
    ergodic theory
    partial differential equations
    calculus of variations
    mathematics
    partial Differential Equations
    calculus of Variations and Optimal Control; Optimization
    dynamical Systems and Ergodic Theory
    analysis
    food Science

    Аннотация: With the goal of establishing a version for partial differential equations (PDEs) of the Aubry–Mather theory of monotone twist maps, Moser and then Bangert studied solutions of their model equations that possessed certain minimality and monotonicity properties. This monograph presents extensions of the Moser–Bangert approach that include solutions of a family of nonlinear elliptic PDEs on Rn and an Allen–Cahn PDE model of phase transitions. After recalling the relevant Moser–Bangert results, Extensions of Moser–Bangert Theory pursues the rich structure of the set of solutions of a simpler model case, expanding upon the studies of Moser and Bangert to include solutions that merely have local minimality properties. Subsequent chapters build upon the introductory results, making the monograph self contained. Part I introduces a variational approach involving a renormalized functional to characterize the basic heteroclinic solutions obtained by Bangert. Following that, Parts II and III employ these basic solutions together with constrained minimization methods to construct multitransition heteroclinic and homoclinic solutions on R×Tn-1 and R2×Tn-2, respectively, as local minima of the renormalized functional. The work is intended for mathematicians who specialize in partial differential equations and may also be used as a text for a graduate topics course in PDEs.
    Доп. точки доступа:
    Stredulinsky, E.W.

    http://dx.doi.org/10.1007/978-0-8176-8117-3


    Держатели документа:
    Государственная публичная научно-техническая библиотека России : 123298, г. Москва, ул. 3-я Хорошевская, д. 17 (Шифр в БД-источнике (KATBW): -979630669)

    Шифр в сводном ЭК: 2328bc786cd6d39601e9ed51f49c1175



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