Result: HETEROCLINIC TRAVELLING WAVES OF GRADIENT DIFFUSION SYSTEMS
Title:
HETEROCLINIC TRAVELLING WAVES OF GRADIENT DIFFUSION SYSTEMS
Authors:
Source:
Transactions of the American Mathematical Society. 363(3):1365-1397
Publisher Information:
Providence, RI: American Mathematical Society, 2011.
Publication Year:
2011
Physical Description:
print, 1 p
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Optimisation et calcul variationnel numériques, Numerical methods in optimization and calculus of variations, Généralités, histoire et biographie, General, history and biography, Mathématiques générales, General mathematics, Branchement, Connecting, Acometida, Compacité, Compactness, Compacidad, Comportement asymptotique, Asymptotic behavior, Comportamiento asintótico, Contrainte, Constraint, Coacción, Diffusion, Difusión, Force, Fuerza, Minimisation fonctionnelle, Functional minimization, Minimización funcional, Méthode variationnelle, Variational methods, Onde progressive, Travelling wave, Onda progresiva, Potentiel, Potential, Potencial, Vitesse déplacement, Speed, Velocidad desplazamiento, 49R50, 65K10, 65Kxx
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ATHENS, PANEPISTIMIOUPOLIS 11584, ATHENS, Greece
INSTITUTE OF APPLIED AND COMPUTATIONAL MATHEMATICS, FOUNDATION FOR RESEARCH AND TECHNOLOGY, 70013 HERAKLION, CRETE, Greece
INSTITUTE OF APPLIED AND COMPUTATIONAL MATHEMATICS, FOUNDATION FOR RESEARCH AND TECHNOLOGY, 70013 HERAKLION, CRETE, Greece
ISSN:
0002-9947
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.23961259
Database:
PASCAL Archive
Further Information
We establish the existence of travelling waves to the gradient system ut = uzz ― ∇W (u) connecting two minima of W when u: ℝ × (0, ∞) → ℝN; that is, we establish the existence of a pair (U,c) ∈ [C2(ℝ)]N x (0,∞), satisfying where a± are local minima of the potential W ∈ C2loc(ℝN) with W(a―) < W(a+) = 0 and N > 1. Our method is variational and based on the minimization of the functional Ec(U) = ∫ℝ{1 2|Ux|2 + W(U)}ecxdx in the appropriate space setup. Following Alikakos and Fusco (2008), we introduce an artificial constraint to restore compactness and force the desired asymptotic behavior, which we later remove. We provide variational characterizations of the travelling wave and the speed.