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Author : Sahbi Keraani
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (493 download)
Download or read book Etude de quelques régimes asymptotiques de l'équation de Schrodinger written by Sahbi Keraani and published by . This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : SAHBI.. KERAANI
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.:/5 (863 download)
Download or read book ETUDE DE QUELQUES REGIMES ASYMPTOTIQUES DE L'EQUATION DE SCHRODINGER written by SAHBI.. KERAANI and published by . This book was released on 2000 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: L'OBJET DE CETTE THESE EST L'ETUDE DE QUELQUES REGIMES ASYMPTOTIQUES DE L'EQUATION DE SCHRODINGER LINEAIRE ET NON LINEAIRE. LES DEUX PREMIERS CHAPITRES SONT CONSACRES A LA DECOMPOSITION EN PROFILS POUR QUELQUES MODELES D'EQUATIONS DE SCHRODINGER LINEAIRES ET NONLINEAIRES. ON MONTRE DES THEOREMES DE STRUCTURES QUI METTENT EN EVIDENCE LE ROLE DES GROUPE DES INVARIANCES DE CES EQUATIONS DANS LES DEFAUTS DE COMPACITE DES FAMILLES D'ESTIMATIONS DE STRICHARTZ ASSOCIEES. CECI NOUS PERMET, EN PARTICULIER, DE MONTRER QUELQUES PROPRIETES DE L'APPLICATION NON LINEAIRE QUI A TOUTE DONNEE INITIALE FAIT ASSOCIER LA SOLUTION DE L'EQUATION DE SCHRODINGER NON LINEAIRE CRITIQUE. LE TROISIEME CHAPITRE EST CONSACRE A L'ETUDE DE LA DYNAMIQUE DE LA MESURE DE WIGNER POUR UNE FAMILLE DE SOLUTIONS DE L'EQUATION DE SCHRODINGER AVEC UN POTENTIEL COULOMBIEN EN DIMENSIONS TROIS DE L'ESPACE. ON MONTRE QUE LA MESURE DE WIGNER SE PROPAGE SELON LES LOIS DE LA MECANIQUE CLASSIQUE : APRES UNE COLLISION AVEC LA SINGULARITE DU POTENTIEL, ELLE EST REFLECHIE SUIVANT LES TRAJECTOIRES REGULARISEES. ENFIN, DANS LE DERNIER CHAPITRE, ON ETUDIE LE COMPORTEMENT ASYMPTOTIQUE QUAND 0 DE L'EQUATION DE SCHRODINGER SEMI-CLASSIQUE, FOCALISANTE, L 2-SOUS CRITIQUE AVEC UN TERME POTENTIEL AYANT UNE DONNEE INITIALE DE LA FORME U (0, X)R(XX 0/) E I X . V 0 / , OU R EST L'ETAT FONDAMENTAL DE L'EQUATION SANS ECHELLE ASSOCIEE (V = 0, = 1). ON MONTRE QUE 1/ D / 2U (T) H 1 1/ D / 2E I P ( T ) + ( T ) / R (. X(T) + Y (T)/) QUAND 0, OU Y : R R D ET : R R SONT DEUX FONCTIONS LOCALEMENT BORNEES ET (X(T), P(T)) LA SOLUTION DU SYSTEME HAMILTONIEN X(T) = P(T), P(T) = *V(X(T)), (X, P) | T = 0 = (X 0, V O). CECI NOUS PERMET, EN PARTICULIER, DE DECRIRE LA DYNAMIQUE DE MESURE DE WIGNER ASSOCIEE A LA FAMILLE 1/ D / 2U (T).
Author : Christian Klein
Publisher : Springer Nature
ISBN 13 : 3030914275
Total Pages : 596 pages
Book Rating : 4.0/5 (39 download)
Download or read book Nonlinear Dispersive Equations written by Christian Klein and published by Springer Nature. This book was released on 2021 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose-Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin-Ono, Davey-Stewartson, and Kadomtsev-Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
Author :
Publisher :
ISBN 13 :
Total Pages : 370 pages
Book Rating : 4.F/5 ( download)
Download or read book Séminaire équations aux dérivées partielles written by and published by . This book was released on 2001 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.3/5 (91 download)
Download or read book Analele Universității Din Craiova written by and published by . This book was released on 2004 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hans G. Feichtinger
Publisher : Springer
ISBN 13 : 3540682686
Total Pages : 235 pages
Book Rating : 4.5/5 (46 download)
Download or read book Pseudo-Differential Operators written by Hans G. Feichtinger and published by Springer. This book was released on 2008-08-15 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.
Author : Semyon Dyatlov
Publisher : American Mathematical Soc.
ISBN 13 : 147044366X
Total Pages : 634 pages
Book Rating : 4.4/5 (74 download)
Download or read book Mathematical Theory of Scattering Resonances written by Semyon Dyatlov and published by American Mathematical Soc.. This book was released on 2019-09-10 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Author :
Publisher :
ISBN 13 :
Total Pages : 644 pages
Book Rating : 4.:/5 (318 download)
Download or read book Séminaire Bourbaki written by and published by . This book was released on 2019 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 1518 pages
Book Rating : 4.X/5 (6 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jean Bourgain
Publisher : American Mathematical Soc.
ISBN 13 : 0821819194
Total Pages : 193 pages
Book Rating : 4.8/5 (218 download)
Download or read book Global Solutions of Nonlinear Schrodinger Equations written by Jean Bourgain and published by American Mathematical Soc.. This book was released on 1999 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with Large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented and several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs.
Author :
Publisher :
ISBN 13 :
Total Pages : 418 pages
Book Rating : 4.:/5 (29 download)
Download or read book The Physics and Chemistry of Solids written by and published by . This book was released on 1958 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : B Vainberg
Publisher : CRC Press
ISBN 13 : 9782881246647
Total Pages : 516 pages
Book Rating : 4.2/5 (466 download)
Download or read book Asymptotic Methods in Equations of Mathematical Physics written by B Vainberg and published by CRC Press. This book was released on 1989-02-25 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Typed English translation of a monograph first published (in Russian) in 1982. Provides graduate students and researchers with usefully detailed discussion of most of the asymptotic methods standard these days to the work of mathematical physicists. The author prefers not to dwell in the heights of abstraction; he has written a broadly intelligble book, which is informed at every point by his secure command of major physical applications. An expensive but valuable contribution to the literature of an important but too-little-written- about field. Twelve chapters, references. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Author : David Lannes
Publisher : American Mathematical Soc.
ISBN 13 : 0821894706
Total Pages : 347 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Water Waves Problem written by David Lannes and published by American Mathematical Soc.. This book was released on 2013-05-08 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.
Author : Mark Fannes
Publisher : Springer Science & Business Media
ISBN 13 : 1461524601
Total Pages : 467 pages
Book Rating : 4.4/5 (615 download)
Download or read book On Three Levels written by Mark Fannes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a five-day NATO Advanced Research Workshop "On Three Levels, the mathematical physics of micro-, meso-, and macro phenomena," conducted from July 19 to 23 in Leuven, Belgium. The main purpose of the workshop was to bring together and to confront where relevant, classical and quantum approaches in the rigorous study of the relation between the various levels of physical description. The reader will find here discussions on a variety of topics involving a broad range of scales. For the micro-level, contributions are presented on models of reaction-diffusion pro cesses, quantum groups and quantum spin systems. The reports on quantum disorder, the quantum Hall effect, semi-classical approaches of wave mechanics and the random Schrodinger equation can be situated on the meso-level. Discussions on macroscopic quantum effects and large scale fluctuations are dealing with the macroscopic level of description. These three levels are however not independent and emphasis is put on relating these scales of description. This is especially the case for the contributions on kinetic and hydrodynamicallimits, the discussions on large deviations and the strong and weak coupling limits. The advisory board was composed of J.L. Lebowitz, J.T. Lewis and E.H. Lieb. The organizing committee was formed by Ph.A. Martin, G.L. Sewell, E.R. Speer and A.
Author : Carlo Cercignani
Publisher : Springer Science & Business Media
ISBN 13 : 1441985247
Total Pages : 357 pages
Book Rating : 4.4/5 (419 download)
Download or read book The Mathematical Theory of Dilute Gases written by Carlo Cercignani and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea for this book was conceived by the authors some time in 1988, and a first outline of the manuscript was drawn up during a summer school on mathematical physics held in Ravello in September 1988, where all three of us were present as lecturers or organizers. The project was in some sense inherited from our friend Marvin Shinbrot, who had planned a book about recent progress for the Boltzmann equation, but, due to his untimely death in 1987, never got to do it. When we drew up the first outline, we could not anticipate how long the actual writing would stretch out. Our ambitions were high: We wanted to cover the modern mathematical theory of the Boltzmann equation, with rigorous proofs, in a complete and readable volume. As the years progressed, we withdrew to some degree from this first ambition- there was just too much material, too scattered, sometimes incomplete, sometimes not rigor ous enough. However, in the writing process itself, the need for the book became ever more apparent. The last twenty years have seen an amazing number of significant results in the field, many of them published in incom plete form, sometimes in obscure places, and sometimes without technical details. We made it our objective to collect these results, classify them, and present them as best we could. The choice of topics remains, of course, subjective.
Author : S. Friedlander
Publisher : Gulf Professional Publishing
ISBN 13 : 008053354X
Total Pages : 627 pages
Book Rating : 4.0/5 (85 download)
Download or read book Handbook of Mathematical Fluid Dynamics written by S. Friedlander and published by Gulf Professional Publishing. This book was released on 2003-03-27 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
Author : Catherine Sulem
Publisher : Springer Science & Business Media
ISBN 13 : 0387227687
Total Pages : 363 pages
Book Rating : 4.3/5 (872 download)
Download or read book The Nonlinear Schrödinger Equation written by Catherine Sulem and published by Springer Science & Business Media. This book was released on 2007-06-30 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.
