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Author: PATRICK-NICOLAS.. PIPOLO
Publisher:
ISBN:
Category :
Languages : fr
Pages : 114
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Book Description
L'OBJET DE CETTE THESE EST L'ETUDE DE PROPRIETES DE REGULARITE DE SOLUTIONS D'EQUATIONS NON LINEAIRES DISPERSIVES. NOUS EN ETUDIONS PARTICULIEREMENT DEUX. CE SONT DES EQUATIONS QUI INTERVIENNENT EN MECANIQUES DES FLUIDES ET EN PHYSIQUE DES PLASMAS. CETTE THESE EST ALORS DIVISEE EN DEUX GRANDES PARTIES : - LA PREMIERE EST CONSACREE A L'ETUDE DE LISSAGE (SMOOTHING) ET ANALYTICITE DE SOLUTIONS AU PROBLEME DE CAUCHY, DE L'EQUATIONS DE SCHRODINGER DE TYPE DERIVATIF EN UNE DIMENSION. - LA SECONDE EST DEDIEE TOUT D'ABORD A L'EXISTENCE D'ONDES SOLITAIRES POUR L'EQUATION KADOMTSEV-PETVIASHVILI GENERALISEE ET ENSUITE A LEUR CARACTERE ANALYTIQUE.
Author: PATRICK-NICOLAS.. PIPOLO
Publisher:
ISBN:
Category :
Languages : fr
Pages : 114
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Book Description
L'OBJET DE CETTE THESE EST L'ETUDE DE PROPRIETES DE REGULARITE DE SOLUTIONS D'EQUATIONS NON LINEAIRES DISPERSIVES. NOUS EN ETUDIONS PARTICULIEREMENT DEUX. CE SONT DES EQUATIONS QUI INTERVIENNENT EN MECANIQUES DES FLUIDES ET EN PHYSIQUE DES PLASMAS. CETTE THESE EST ALORS DIVISEE EN DEUX GRANDES PARTIES : - LA PREMIERE EST CONSACREE A L'ETUDE DE LISSAGE (SMOOTHING) ET ANALYTICITE DE SOLUTIONS AU PROBLEME DE CAUCHY, DE L'EQUATIONS DE SCHRODINGER DE TYPE DERIVATIF EN UNE DIMENSION. - LA SECONDE EST DEDIEE TOUT D'ABORD A L'EXISTENCE D'ONDES SOLITAIRES POUR L'EQUATION KADOMTSEV-PETVIASHVILI GENERALISEE ET ENSUITE A LEUR CARACTERE ANALYTIQUE.
Author: JACQUES.. SIMON
Publisher:
ISBN:
Category :
Languages : fr
Pages : 160
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Book Description
QUELQUES PROPRIETES DE SOLUTIONS D'EQUATIONS ET D'INEQUATIONS D'EVOLUTION PARABOLIQUES NON LINEAIRES. REGULARITE DE LA COMPOSEE DE DEUX FONCTIONS ET APPLICATIONS. REGULARITE DE LA SOLUTION D'UNE EQUATION NON LINEAIRE DANS R**(N). CARACTERISATION D'ESPACES FONCTIONNELS. REGULARITE LOCALE DES SOLUTIONS D'UNE EQUATION NON LINEAIRE. REGULARITE DE LA SOLUTION D'UN PROBLEME AUX LIMITES NON LINEAIRES.
Author: Laziz Abdelouhab
Publisher:
ISBN:
Category :
Languages : fr
Pages : 136
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Book Description
On étudie la régularité des solutions du problème de Cauchy associé à certaines équations dispersives non linéaires non locales: l'équation de Benjamin-Ono (B.O) et l'équation des grandes ondes internes en profondeur finie (O. L. I). On écrit d'abord les multiplicateurs qui conduisent à quelques invariants de l'équation de Benjamin-Ono obtenus par K.M. Case (1979) ; puis utilisant la technique de régularisation parabolique on démontre que: pour toute donnée initiale, l'équation de Benjamin-Ono ou des ondes internes en profondeur finie possède une solution unique, de plus la solution dépend continûment de la donnée initiale. On démontre aussi des résultats d'existence globale en temps. L'équation des ondes internes est traitée comme une perturbation de l'équation de Benjamin-Ono. On montre que les solutions des équations intermédiaires convergent vers la solution de l'équation de Benjamin-Ono lorsque la profondeur devient infinie alors que l'équation des ondes internes se réduit formellement a celle de Koeteweg-de-Vries dans la surface limite. On discute aussi le problème périodique - en espace - associé à chacune de ces équations.
Author:
Publisher:
ISBN:
Category : Information science
Languages : en
Pages : 392
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Author:
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : fr
Pages : 370
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Book Description
Author: T. Alazard
Publisher: American Mathematical Soc.
ISBN: 147043203X
Category : Mathematics
Languages : en
Pages : 120
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Book Description
This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to L2. The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.
Author: Jaime Angulo Pava
Publisher: American Mathematical Soc.
ISBN: 0821848976
Category : Mathematics
Languages : en
Pages : 272
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Book Description
This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied include Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.
Author: Massimiliano Gubinelli
Publisher: Springer Nature
ISBN: 3030295451
Category : Mathematics
Languages : en
Pages : 316
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Book Description
Written by leading experts in an emerging field, this book offers a unique view of the theory of stochastic partial differential equations, with lectures on the stationary KPZ equation, fully nonlinear SPDEs, and random data wave equations. This subject has recently attracted a great deal of attention, partly as a consequence of Martin Hairer's contributions and in particular his creation of a theory of regularity structures for SPDEs, for which he was awarded the Fields Medal in 2014. The text comprises three lectures covering: the theory of stochastic Hamilton–Jacobi equations, one of the most intriguing and rich new chapters of this subject; singular SPDEs, which are at the cutting edge of innovation in the field following the breakthroughs of regularity structures and related theories, with the KPZ equation as a central example; and the study of dispersive equations with random initial conditions, which gives new insights into classical problems and at the same time provides a surprising parallel to the theory of singular SPDEs, viewed from many different perspectives. These notes are aimed at graduate students and researchers who want to familiarize themselves with this new field, which lies at the interface between analysis and probability.
Author: Lars Hörmander
Publisher: Springer Science & Business Media
ISBN: 1461207754
Category : Mathematics
Languages : en
Pages : 384
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Book Description
On March 17-19 and May 19-21,1995, analysis seminars were organized jointly at the universities of Copenhagen and Lund, under the heading "Danish-Swedish Analysis Seminar". The main topic was partial differen tial equations and related problems of mathematical physics. The lectures given are presented in this volume, some as short abstracts and some as quite complete expositions or survey papers. They span over a large vari ety of topics. The most frequently occurring theme is the use of microlocal analysis which is now important also in the study of non-linear differential equations although it originated entirely within the linear theory. Perhaps it is less surprising that microlocal analysis has proved to be useful in the study of mathematical problems of classical quantum mechanics, for it re ceived a substantial input of ideas from that field. The scientific committee for the invitation of speakers consisted of Gerd Grubb in Copenhagen, Lars Hormander and Anders MeHn in Lund, and Jo hannes Sjostrand in Paris. Lars Hormander and Anders Melin have edited the proceedings. They were hosts of the seminar days in Lund while Gerd Grubb was the host in Copenhagen. Financial support was obtained from the mathematics departments in Copenhagen and Lund, CNRS in France, the Danish and Swedish Na tional Research Councils, Gustaf Sigurd Magnuson's foundation at the Royal Swedish Academy of Sciences, and the Wenner-Gren foundation in Stockholm. We want to thank all these organisations for their support
Author: Carlo Cercignani
Publisher: Springer Science & Business Media
ISBN: 1441985247
Category : Science
Languages : en
Pages : 357
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Book Description
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.
