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Author: Pascal Bégout
Publisher: Omniscriptum
ISBN: 9786131534591
Category :
Languages : en
Pages : 128
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Book Description
Les travaux pr sent s dans cette th se concerne l' quation de Schr dinger avec puissance simple comme non-lin arit . Dans une premi re partie, on tudie des solutions globales en temps poss dant un tat de diffusion dans un espace de Sobolev poids. Puisque le groupe de Schr dinger n'est pas une isom trie sur cet espace, on cherche savoir si de telles solutions convergent vers leur tat de diffusion. La r ciproque est galement tudi e. Dans une deuxi me partie, on montre que la vitesse maximale de d croissance en temps des solutions est celle des solutions du probl me lin aire associ . Une troisi me partie traite de conditions suffisantes et de conditions n cessaires pour l'existence globale en temps de solutions dans le cas surcritique. Dans une quatri me partie, on simplifie la d monstration d'un r sultat de Kenji Nakanishi. Dans une derni re partie, on regarde la r gularit de certaines solutions auto-similaires.
Author: Pascal Bégout
Publisher: Omniscriptum
ISBN: 9786131534591
Category :
Languages : en
Pages : 128
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Book Description
Les travaux pr sent s dans cette th se concerne l' quation de Schr dinger avec puissance simple comme non-lin arit . Dans une premi re partie, on tudie des solutions globales en temps poss dant un tat de diffusion dans un espace de Sobolev poids. Puisque le groupe de Schr dinger n'est pas une isom trie sur cet espace, on cherche savoir si de telles solutions convergent vers leur tat de diffusion. La r ciproque est galement tudi e. Dans une deuxi me partie, on montre que la vitesse maximale de d croissance en temps des solutions est celle des solutions du probl me lin aire associ . Une troisi me partie traite de conditions suffisantes et de conditions n cessaires pour l'existence globale en temps de solutions dans le cas surcritique. Dans une quatri me partie, on simplifie la d monstration d'un r sultat de Kenji Nakanishi. Dans une derni re partie, on regarde la r gularit de certaines solutions auto-similaires.
Author: Pascal Bégout
Publisher:
ISBN:
Category :
Languages : en
Pages : 130
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Book Description
Author: Pascal Bégout
Publisher:
ISBN:
Category :
Languages : fr
Pages : 0
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Author: Olivier Bouchel
Publisher:
ISBN:
Category :
Languages : en
Pages : 144
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Book Description
This PhD thesis is devoted to a few nonlinear Schrödinger equations and systems. The nonlinear Schrödinger equation is one of themost important models in the description of phenomena in nonlinear optics, in superfluidity or in supra-conductivity. Deriving fromphysics equations one more accurate form of the nonlinear Schrödinger equation, we get one additional fourth order anisotropic dispersion term in the time variable : in the first and in the fifth sections, we study for this equation the Cauchy problems in suitable spaces, the existence and qualitative properties of its solitary waves, stability and blowup issues, theoretically as well as numerically.In the third section, considering the example of one system of coupled nonlinear Schrödinger equations arising in nonlinear optics, we investigate the existence of solitary waves and their symmetry properties.In the second and fourth sections, non zero boundary conditions in some nonlinear Schrödinger equations are required : this issue,which appears naturally in the Bose Einstein condensation theory, is illustrated with the study of the asymptotic behaviour of oneGross-Pitaevskii-Schrödinger system, and of the existence of nonstationary bubbles in dimensions two and three.
Author: Anne de Bouard
Publisher:
ISBN:
Category :
Languages : fr
Pages :
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Book Description
CETTE THESE EST CONSTITUEE DE TROIS PARTIES PORTANT CHACUNE SUR L'ETUDE DE CERTAINES PROPRIETES D'EQUATIONS D'ONDES NON LINEAIRE DISPERSIVES DE TYPE SCHRODINGER INTERVENANT DANS DIFFERENTS DOMAINES DE LA PHYSIQUE. DANS LA PREMIERE PARTIE, ON ETUDIE LE PROBLEME DE CAUCHY ASSOCIE A UNE EQUATION DE SCHRODINGER NON LINEAIRE EN PRESENCE D'UN CHAMP MAGNETIQUE EXTERNE. SOUS CERTAINES RESTRICTIONS DE CROISSANCE SUR LES POTENTIELS APPARAISSANT DANS L'EQUATION ET SUR LE TERME NON LINEAIRE, ON MONTRE L'EXISTENCE LOCALE EN TEMPS ET L'UNICITE DES SOLUTIONS DU PROBLEME DE CAUCHY POUR CETTE EQUATION DANS DES ESPACES DE TYPE SOBOLEV A POIDS, AINSI QUE LA CONSERVATION DE L'ENERGIE ASSOCIEE A L'EQUATION. DANS LA SECONDE PARTIE, ON ETUDIE L'EXISTENCE DE SOLUTIONS ANALYTIQUES TRES REGULIERES POUR UNE EQUATION DE TYPE SCHRODINGER NON LINEAIRE ASSEZ GENERALE, ENGLOBANT UN CERTAIN NOMBRE DE MODELES PHYSIQUES REGISSANT LE MOUVEMENT DES ONDES AQUATIQUES DE SURFACE, DANS LESQUELS LE TERME LINEAIRE PEUT ETRE UN OPERATEUR DIFFERENTIEL D'ORDRE SUPERIEUR A DEUX, ET FAISANT EVENTUELLEMENT INTERVENIR UN TERME NON LINEAIRE NON LOCAL. LA TROISIEME PARTIE EST CONSACREE A L'ETUDE DE L'EXISTENCE ET DE L'INSTABILITE DE CERTAINES SOLUTIONS STATIONNAIRES LOCALISEES D'UNE EQUATION DE SCHRODINGER NON LINEAIRE DANS LAQUELLE LA NON-LINEARITE EST RELATIVEMENT GENERALE. CES SOLUTIONS GENERALISEES ONT LA PARTICULARITE D'AVOIR UNE LIMITE NON NULLE LORSQUE LA VARIABLE D'ESPACE TEND VERS L'INFINI, ET PEUVENT ETRE INTERPRETEES PHYSIQUEMENT LORSQUE LE TERME NON LINEAIRE EST BIEN CHOISI. ON MONTRE EN LINEARISANT L'EQUATION QUE, LORSQU'ELLES EXISTENT, CES SOLUTIONS GENERALISEES SONT TOUJOURS DES SOLUTIONS INSTABLES DE L'EQUATION D'EVOLUTION
Author:
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ISBN:
Category : Physics
Languages : en
Pages : 632
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Author: Peter E. Zhidkov
Publisher: Springer
ISBN: 3540452761
Category : Mathematics
Languages : en
Pages : 153
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Book Description
- of nonlinear the of solitons the the last 30 theory partial theory During years - has into solutions of a kind a differential special equations (PDEs) possessing grown and in view the attention of both mathematicians field that attracts physicists large and of the of the problems of its novelty problems. Physical important applications for in the under consideration are mo- to the observed, example, equations leading mathematical discoveries is the Makhankov One of the related V.G. by [60]. graph from this field methods that of certain nonlinear by equations possibility studying inverse these to the problem; equations were analyze quantum scattering developed this method of the inverse called solvable the scattering problem (on subject, are by known nonlinear At the the class of for same time, currently example [89,94]). see, the other there is solvable this method is narrow on hand, PDEs sufficiently and, by of differential The latter called the another qualitative theory equations. approach, the of various in includes on pr- investigations well-posedness approach particular solutions such or lems for these the behavior of as stability blowing-up, equations, these and this of approach dynamical systems generated by equations, etc., properties in wider class of a makes it to an problems (maybe possible investigate essentially more general study).
Author: Alexander A. Kovalevsky
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110332248
Category : Mathematics
Languages : en
Pages : 448
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Book Description
This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form. The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis. Contents: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography
Author: James Serrin
Publisher: American Mathematical Soc.
ISBN: 0821898612
Category : Mathematics
Languages : en
Pages : 354
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Book Description
This book is the second of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honour of Patrizia Pucci's 60th birthday. The workshop brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants.
Author: Vincenzo Ambrosio
Publisher: Springer Nature
ISBN: 3030602206
Category : Mathematics
Languages : en
Pages : 669
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Book Description
This monograph presents recent results concerning nonlinear fractional elliptic problems in the whole space. More precisely, it investigates the existence, multiplicity and qualitative properties of solutions for fractional Schrödinger equations by applying suitable variational and topological methods. The book is mainly intended for researchers in pure and applied mathematics, physics, mechanics, and engineering. However, the material will also be useful for students in higher semesters and young researchers, as well as experienced specialists working in the field of nonlocal PDEs. This is the first book to approach fractional nonlinear Schrödinger equations by applying variational and topological methods.
