Extensions of Moser–Bangert Theory

Locally Minimal Solutions

AvPaul H. Rabinowitz,Edward W. Stredulinsky

Inbunden, Engelska, 2011

Del i serien Progress in Nonlinear Differential Equations and Their Applications

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Beskrivning

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.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.

Produktinformation

Utgivningsdatum:2011-06-24
Mått:155 x 235 x undefined mm
Vikt:468 g
Format:Inbunden
Språk:Engelska
Serie:Progress in Nonlinear Differential Equations and Their Applications
Antal sidor:208
Upplaga:2011
Förlag:Birkhauser Boston Inc
ISBN:9780817681166

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Recensioner i media

From the reviews: "This book contains a study of the solution set to (PDE), expanding work by Moser and Bangert and previous work by the authors for (AC). ... This is an important piece of work concerning a difficult and deep matter. ... This a very good demonstration of the power of variational methods, showing that they can be modified, extended and combined in order to deal with many different kinds of problems." (Jesus Hernandez, Mathematical Reviews, Issue 2012 m)

Innehållsförteckning

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^2 x T^{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