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Autor Rabinowitz, Paul H. author.

Título Extensions of Moseŕァngert Theory [electronic resource] : Locally Minimal Solutions / by Paul H. Rabinowitz, Edward W. Stredulinsky.

Publicación Boston : Birkhäuser Boston, 2011.
Descripción física VIII, 208 p. online resource.
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Colección Progress in Nonlinear Differential Equations and Their Applications ; 81
Progress in Nonlinear Differential Equations and Their Applications ; 81
Springer eBooks. Mathematics and Statistics
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Contiene: 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 R̂2 x T̂{n-2} -- 12 A Class of Strictly 1-Monotone Infinite Transition Solutions of (PDE) -- 13 Solutions of (PDE) with Two Transitions in x1 and Heteroclinic Behavior in x2.
Resumen: With the goal of establishing a version for partial differential equations (PDEs) of the Aubrý㍡ther 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 Moseŕァngert approach that include solutions of a family of nonlinear elliptic PDEs on Rn and an Alleńメhn PDE model of phase transitions. After recalling the relevant Moseŕァngert results, Extensions of Moseŕァngert 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.
Materia Mathematics.
Food -- Biotechnology.
Análisis matemático
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Analysis (Mathematics).
Ergodic theory.
Partial differential equations.
Calculus of variations.
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Partial Differential Equations.
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Calculus of Variations and Optimal Control; Optimization.
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Dynamical Systems and Ergodic Theory.
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Food Science.
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Autor secundario Stredulinsky, Edward W., author.
SpringerLink (Online service)
En Springer eBooks
OTRO SOPORTE Printed edition: 9780817681166
ISBN 9780817681173 978-0-8176-8117-3
ISBN/ISSN 10.1007/978-0-8176-8117-3 doi