A compactness result for inhomogeneous ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
A compactness result for inhomogeneous nonlinear Schrödinger equations
Author(s) :
Dinh, Van [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Ho Chi Minh City University of Science [HCMUS]
Keraani, Sahbi [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Ho Chi Minh City University of Science [HCMUS]
Keraani, Sahbi [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Journal title :
Nonlinear Analysis: Theory, Methods and Applications
Pages :
112617
Publisher :
Elsevier
Publication date :
2022
ISSN :
0362-546X
English keyword(s) :
Inhomogeneous nonlinear Schrödinger equation
Compactness property
Linear profile decomposition
Nonlinear profile decomposition
Compactness property
Linear profile decomposition
Nonlinear profile decomposition
HAL domain(s) :
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Physique mathématique [math-ph]
English abstract : [en]
We establish a compactness property of the difference between nonlinear and linear operators (or the Duhamel operator) related to the inhomogeneous nonlinear Schr¨odinger equation. The proof is based on a refined profile ...
Show more >We establish a compactness property of the difference between nonlinear and linear operators (or the Duhamel operator) related to the inhomogeneous nonlinear Schr¨odinger equation. The proof is based on a refined profile decomposition for the equation. More precisely, we prove that any sequence (φn)n of H1-functions which converges weakly in H1 to a function φ, the corresponding solutions with initial data φn can be decomposed (up to a remainder term) as a sum of the corresponding solution with initial data φ and solutions to the linear equationShow less >
Show more >We establish a compactness property of the difference between nonlinear and linear operators (or the Duhamel operator) related to the inhomogeneous nonlinear Schr¨odinger equation. The proof is based on a refined profile decomposition for the equation. More precisely, we prove that any sequence (φn)n of H1-functions which converges weakly in H1 to a function φ, the corresponding solutions with initial data φn can be decomposed (up to a remainder term) as a sum of the corresponding solution with initial data φ and solutions to the linear equationShow less >
Language :
Anglais
Popular science :
Non
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