Analysis Of Hamiltonian Pdes

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Analysis of Hamiltonian PDEs

Author : Sergej B. Kuksin
Publisher : Clarendon Press
ISBN 13 : 9780198503958
Total Pages : 228 pages
Book Rating : 4.5/5 (39 download)

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Book Synopsis Analysis of Hamiltonian PDEs by : Sergej B. Kuksin

Download or read book Analysis of Hamiltonian PDEs written by Sergej B. Kuksin and published by Clarendon Press. This book was released on 2000 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the last 20-30 years, interest among mathematicians and physicists in infinite-dimensional Hamiltonian systems and Hamiltonian partial differential equations has been growing strongly, and many papers and a number of books have been written on integrable Hamiltonian PDEs. During the last decade though, the interest has shifted steadily towards non-integrable Hamiltonian PDEs. Here, not algebra but analysis and symplectic geometry are the appropriate analysing tools. The present book is the first one to use this approach to Hamiltonian PDEs and present a complete proof of the "KAM for PDEs" theorem. It will be an invaluable source of information for postgraduate mathematics and physics students and researchers.

Nonlinear Oscillations of Hamiltonian PDEs

Author : Massimiliano Berti
Publisher : Springer Science & Business Media
ISBN 13 : 0817646809
Total Pages : 191 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Nonlinear Oscillations of Hamiltonian PDEs by : Massimiliano Berti

Download or read book Nonlinear Oscillations of Hamiltonian PDEs written by Massimiliano Berti and published by Springer Science & Business Media. This book was released on 2007-10-01 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. The text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.

Long-time Analysis of Hamiltonian Partial Differential Equations and Their Discretizations

Author : Ludwig Gauckler
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (649 download)

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Book Synopsis Long-time Analysis of Hamiltonian Partial Differential Equations and Their Discretizations by : Ludwig Gauckler

Download or read book Long-time Analysis of Hamiltonian Partial Differential Equations and Their Discretizations written by Ludwig Gauckler and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hamiltonian Partial Differential Equations and Applications

Author : Philippe Guyenne
Publisher : Springer
ISBN 13 : 149392950X
Total Pages : 453 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Hamiltonian Partial Differential Equations and Applications by : Philippe Guyenne

Download or read book Hamiltonian Partial Differential Equations and Applications written by Philippe Guyenne and published by Springer. This book was released on 2015-09-11 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

Hamiltonian Dynamical Systems and Applications

Author : Walter Craig
Publisher : Springer Science & Business Media
ISBN 13 : 1402069642
Total Pages : 450 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Hamiltonian Dynamical Systems and Applications by : Walter Craig

Download or read book Hamiltonian Dynamical Systems and Applications written by Walter Craig and published by Springer Science & Business Media. This book was released on 2008-02-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Phase Space Analysis of Partial Differential Equations

Author : Antonio Bove
Publisher : Springer Science & Business Media
ISBN 13 : 0817645217
Total Pages : 336 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Phase Space Analysis of Partial Differential Equations by : Antonio Bove

Download or read book Phase Space Analysis of Partial Differential Equations written by Antonio Bove and published by Springer Science & Business Media. This book was released on 2007-12-28 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers phase space analysis methods, including microlocal analysis, and their applications to physics Treats the linear and nonnlinear aspects of the theory of PDEs Original articles are self-contained with full proofs; survey articles give a quick and direct introduction to selected topics evolving at a fast pace Excellent reference and resource for grad students and researchers in PDEs and related fields

Attractors of Hamiltonian Nonlinear Partial Differential Equations

Author : Alexander Komech
Publisher : Cambridge University Press
ISBN 13 : 100903605X
Total Pages : pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Attractors of Hamiltonian Nonlinear Partial Differential Equations by : Alexander Komech

Download or read book Attractors of Hamiltonian Nonlinear Partial Differential Equations written by Alexander Komech and published by Cambridge University Press. This book was released on 2021-09-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh's convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.

Hamiltonian Systems with Three or More Degrees of Freedom

Author : Carles Simó
Publisher : Springer Science & Business Media
ISBN 13 : 940114673X
Total Pages : 681 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Hamiltonian Systems with Three or More Degrees of Freedom by : Carles Simó

Download or read book Hamiltonian Systems with Three or More Degrees of Freedom written by Carles Simó and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.

Port-Hamiltonian Systems Theory

Author : Schaft Van Der
Publisher :
ISBN 13 : 9781601987860
Total Pages : 230 pages
Book Rating : 4.9/5 (878 download)

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Book Synopsis Port-Hamiltonian Systems Theory by : Schaft Van Der

Download or read book Port-Hamiltonian Systems Theory written by Schaft Van Der and published by . This book was released on 2014-06-13 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Port-Hamiltonian Systems Theory: An Introductory Overview provides a concise and easily accessible description of the foundations underpinning the subject and emphasizes novel developments in the field, which will be of interest to a broad range of researchers.

Variational Methods

Author : Michael Struwe
Publisher : Springer Science & Business Media
ISBN 13 : 3662032120
Total Pages : 288 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Variational Methods by : Michael Struwe

Download or read book Variational Methods written by Michael Struwe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radò. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field.

Hamiltonian Dynamics - Theory and Applications

Author : Giancarlo Benettin
Publisher : Springer
ISBN 13 : 3540315411
Total Pages : 187 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Hamiltonian Dynamics - Theory and Applications by : Giancarlo Benettin

Download or read book Hamiltonian Dynamics - Theory and Applications written by Giancarlo Benettin and published by Springer. This book was released on 2005-01-14 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume compiles three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants, and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.

Geometry in Partial Differential Equations

Author : Agostino Prastaro
Publisher : World Scientific
ISBN 13 : 9789810214074
Total Pages : 482 pages
Book Rating : 4.2/5 (14 download)

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Book Synopsis Geometry in Partial Differential Equations by : Agostino Prastaro

Download or read book Geometry in Partial Differential Equations written by Agostino Prastaro and published by World Scientific. This book was released on 1994 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.

Partial Differential Equations and Functional Analysis

Author : Andrew Comech
Publisher : Springer Nature
ISBN 13 : 303133681X
Total Pages : 334 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Partial Differential Equations and Functional Analysis by : Andrew Comech

Download or read book Partial Differential Equations and Functional Analysis written by Andrew Comech and published by Springer Nature. This book was released on 2023-11-15 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mark Vishik was one of the prominent figures in the theory of partial differential equations. His ground-breaking contributions were instrumental in integrating the methods of functional analysis into this theory. The book is based on the memoirs of his friends and students, as well as on the recollections of Mark Vishik himself, and contains a detailed description of his biography: childhood in Lwów, his connections with the famous Lwów school of Stefan Banach, a difficult several year long journey from Lwów to Tbilisi after the Nazi assault in June 1941, going to Moscow and forming his own school of differential equations, whose central role was played by the famous Vishik Seminar at the Department of Mechanics and Mathematics at Moscow State University. The reader is introduced to a number of remarkable scientists whose lives intersected with Vishik’s, including S. Banach, J. Schauder, I. N. Vekua, N. I. Muskhelishvili, L. A. Lyusternik, I. G. Petrovskii, S. L. Sobolev, I. M. Gelfand, M. G. Krein, A. N. Kolmogorov, N. I. Akhiezer, J. Leray, J.-L. Lions, L. Schwartz, L. Nirenberg, and many others. The book also provides a detailed description of the main research directions of Mark Vishik written by his students and colleagues, as well as several reviews of the recent development in these directions.

Hamiltonian Dynamics Theory and Applications

Author : CIME-EMS Summer School (
Publisher : Springer Science & Business Media
ISBN 13 : 9783540240648
Total Pages : 196 pages
Book Rating : 4.2/5 (46 download)

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Book Synopsis Hamiltonian Dynamics Theory and Applications by : CIME-EMS Summer School (

Download or read book Hamiltonian Dynamics Theory and Applications written by CIME-EMS Summer School ( and published by Springer Science & Business Media. This book was released on 2005 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Solving PDEs in Python

Author : Hans Petter Langtangen
Publisher : Springer
ISBN 13 : 3319524623
Total Pages : 152 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Solving PDEs in Python by : Hans Petter Langtangen

Download or read book Solving PDEs in Python written by Hans Petter Langtangen and published by Springer. This book was released on 2017-03-21 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.

Nearly Integrable Infinite-Dimensional Hamiltonian Systems

Author : Sergej B. Kuksin
Publisher : Springer
ISBN 13 : 3540479201
Total Pages : 128 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Nearly Integrable Infinite-Dimensional Hamiltonian Systems by : Sergej B. Kuksin

Download or read book Nearly Integrable Infinite-Dimensional Hamiltonian Systems written by Sergej B. Kuksin and published by Springer. This book was released on 2006-11-15 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to partial differential equations of Hamiltonian form, close to integrable equations. For such equations a KAM-like theorem is proved, stating that solutions of the unperturbed equation that are quasiperiodic in time mostly persist in the perturbed one. The theorem is applied to classical nonlinear PDE's with one-dimensional space variable such as the nonlinear string and nonlinear Schr|dinger equation andshow that the equations have "regular" (=time-quasiperiodic and time-periodic) solutions in rich supply. These results cannot be obtained by other techniques. The book will thus be of interest to mathematicians and physicists working with nonlinear PDE's. An extensivesummary of the results and of related topics is provided in the Introduction. All the nontraditional material used is discussed in the firstpart of the book and in five appendices.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Author : Haim Brezis
Publisher : Springer Science & Business Media
ISBN 13 : 0387709142
Total Pages : 600 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Functional Analysis, Sobolev Spaces and Partial Differential Equations by : Haim Brezis

Download or read book Functional Analysis, Sobolev Spaces and Partial Differential Equations written by Haim Brezis and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.