Quasi Linear Perturbations Of Hamiltonian Klein Gordon Equations On Spheres

Quasi Linear Perturbations of Hamiltonian Klein Gordon Equations on Spheres PDF
Author: J.-M. Delort
Publisher: American Mathematical Soc.
ISBN: 1470409836
Size: 28.72 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 80
View: 5589

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Quasi Linear Perturbations Of Hamiltonian Klein Gordon Equations On Spheres

by J.-M. Delort, Quasi Linear Perturbations Of Hamiltonian Klein Gordon Equations On Spheres Books available in PDF, EPUB, Mobi Format. Download Quasi Linear Perturbations Of Hamiltonian Klein Gordon Equations On Spheres books, The Hamiltonian ∫X(∣∂tu∣2+∣∇u∣2+m2∣u∣2)dx, defined on functions on R×X, where X is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. The author considers perturbations of this Hamiltonian, given by polynomial expressions depending on first order derivatives of u. The associated PDE is then a quasi-linear Klein-Gordon equation. The author shows that, when X is the sphere, and when the mass parameter m is outside an exceptional subset of zero measure, smooth Cauchy data of small size ϵ give rise to almost global solutions, i.e. solutions defined on a time interval of length cNϵ−N for any N. Previous results were limited either to the semi-linear case (when the perturbation of the Hamiltonian depends only on u) or to the one dimensional problem. The proof is based on a quasi-linear version of the Birkhoff normal forms method, relying on convenient generalizations of para-differential calculus.



Almost Global Solutions Of Capillary Gravity Water Waves Equations On The Circle

Almost Global Solutions of Capillary Gravity Water Waves Equations on the Circle PDF
Author: Massimiliano Berti
Publisher: Springer
ISBN: 3319994867
Size: 19.14 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 269
View: 2371

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Almost Global Solutions Of Capillary Gravity Water Waves Equations On The Circle

by Massimiliano Berti, Almost Global Solutions Of Capillary Gravity Water Waves Equations On The Circle Books available in PDF, EPUB, Mobi Format. Download Almost Global Solutions Of Capillary Gravity Water Waves Equations On The Circle books, The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.



Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes

Proceedings Of The International Congress Of Mathematicians 2018  Icm 2018   In 4 Volumes  PDF
Author: Sirakov Boyan
Publisher: World Scientific
ISBN: 9813272899
Size: 19.18 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 5396
View: 6488

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Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes

by Sirakov Boyan, Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes Books available in PDF, EPUB, Mobi Format. Download Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes books, The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.



Diffraction Of Singularities For The Wave Equation On Manifolds With Corners

Diffraction of Singularities for the Wave Equation on Manifolds with Corners PDF
Author: Richard B. Melrose
Publisher: Amer Mathematical Society
ISBN:
Size: 14.69 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 135
View: 4194

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Diffraction Of Singularities For The Wave Equation On Manifolds With Corners

by Richard B. Melrose, Diffraction Of Singularities For The Wave Equation On Manifolds With Corners Books available in PDF, EPUB, Mobi Format. Download Diffraction Of Singularities For The Wave Equation On Manifolds With Corners books, The authors consider the fundamental solution to the wave equation on a manifold with corners of arbitrary codimension. If the initial pole of the solution is appropriately situated, the authors show that the singularities which are diffracted by the corners (i.e., loosely speaking, are not propagated along limits of transversely reflected rays) are smoother than the main singularities of the solution. More generally, the authors show that subject to a hypothesis of nonfocusing, diffracted wavefronts of any solution to the wave equation are smoother than the incident singularities. These results extend the authors' previous work on edge manifolds to a situation where the fibers of the boundary fibration, obtained here by blowup of the corner in question, are themselves manifolds with corners.



Handbook Of Dynamical Systems

Handbook of Dynamical Systems PDF
Author: H. Broer
Publisher: Elsevier
ISBN: 9780080932262
Size: 79.36 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 560
View: 4168

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Handbook Of Dynamical Systems

by H. Broer, Handbook Of Dynamical Systems Books available in PDF, EPUB, Mobi Format. Download Handbook Of Dynamical Systems books, In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems Highlights developments that are the foundation for future research in this field Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems



Mathematical Reviews

Mathematical Reviews PDF
Author:
Publisher:
ISBN:
Size: 64.17 MB
Format: PDF
Category : Mathematics
Languages : en
Pages :
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Mathematical Reviews

by , Mathematical Reviews Books available in PDF, EPUB, Mobi Format. Download Mathematical Reviews books,



Analysis Modeling And Simulation Of Multiscale Problems

Analysis  Modeling and Simulation of Multiscale Problems PDF
Author: Alexander Mielke
Publisher: Springer Science & Business Media
ISBN: 3540356576
Size: 39.37 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 697
View: 4924

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Analysis Modeling And Simulation Of Multiscale Problems

by Alexander Mielke, Analysis Modeling And Simulation Of Multiscale Problems Books available in PDF, EPUB, Mobi Format. Download Analysis Modeling And Simulation Of Multiscale Problems books, This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.



Hamiltonian Dynamical Systems And Applications

Hamiltonian Dynamical Systems and Applications PDF
Author: Walter Craig
Publisher: Springer Science & Business Media
ISBN: 1402069642
Size: 41.48 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 441
View: 7143

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Hamiltonian Dynamical Systems And Applications

by Walter Craig, Hamiltonian Dynamical Systems And Applications Books available in PDF, EPUB, Mobi Format. Download Hamiltonian Dynamical Systems And Applications books, This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.



Introduction To Asymptotic Methods

Introduction to Asymptotic Methods PDF
Author: David Y. Gao
Publisher: CRC Press
ISBN: 9781420011739
Size: 31.50 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 272
View: 981

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Introduction To Asymptotic Methods

by David Y. Gao, Introduction To Asymptotic Methods Books available in PDF, EPUB, Mobi Format. Download Introduction To Asymptotic Methods books, Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m