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Extensions of Moser-Bangert Theory : Locally Minimal Solutions

Author: Paul H Rabinowitz; Edward W Stredulinsky
Publisher: Boston : Birkhäuser Boston, 2011.
Series: Progress in nonlinear differential equations and their applications, 81.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Paul H Rabinowitz; Edward W Stredulinsky
ISBN: 9780817681173 0817681175 9780817681166 0817681167
OCLC Number: 779195448
Description: 1 online resource.
Contents: 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.
Series Title: Progress in nonlinear differential equations and their applications, 81.
Responsibility: by Paul H. Rabinowitz, Edward W. Stredulinsky.

Abstract:

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. The text may be  Read more...

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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 Read more...

 
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