Hamiltonian Partial Differential Equations And Applications
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Nonlinear Oscillations Of Hamiltonian Pdes
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Author : Massimiliano Berti
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-01
Nonlinear Oscillations Of Hamiltonian Pdes written by Massimiliano Berti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-01 with Mathematics categories.
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.
Analysis Of Hamiltonian Pdes
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Author : Sergej B. Kuksin
language : en
Publisher: Clarendon Press
Release Date : 2000
Analysis Of Hamiltonian Pdes written by Sergej B. Kuksin and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
Hamiltonian Partial Differential Equations And Applications
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Author : Philippe Guyenne
language : en
Publisher: Springer
Release Date : 2015-09-11
Hamiltonian Partial Differential Equations And Applications written by Philippe Guyenne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-11 with Mathematics categories.
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.
Variational Methods
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Author : Michael Struwe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Variational Methods written by Michael Struwe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
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 Dynamical Systems And Applications
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Author : Walter Craig
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-17
Hamiltonian Dynamical Systems And Applications written by Walter Craig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-17 with Mathematics categories.
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.
Geometry In Partial Differential Equations
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Author : Agostino Prastaro
language : en
Publisher: World Scientific
Release Date : 1994
Geometry In Partial Differential Equations written by Agostino Prastaro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
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.
The Action Principle And Partial Differential Equations
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Author : Demetrios Christodoulou
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
The Action Principle And Partial Differential Equations written by Demetrios Christodoulou and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and Hamilton-Jacobi theory for Lagrangian systems of ordinary differential equations. A distinguishing characteristic of this approach is that one considers, at once, entire families of solutions of the Euler-Lagrange equations, rather than restricting attention to single solutions at a time. The second part of the book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E. Noether. Finally, the third part introduces a new general definition of hyperbolicity, based on a quadratic form associated with the Lagrangian, which overcomes the obstacles arising from singularities of the characteristic variety that were encountered in previous approaches. On the basis of the new definition, the domain-of-dependence theorem and stability properties of solutions are derived. Applications to continuum mechanics are discussed throughout the book. The last chapter is devoted to the electrodynamics of nonlinear continuous media.
Variational Methods
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Author : Michael Struwe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Variational Methods written by Michael Struwe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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 Radó. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The third edition gives a survey on new developments in the field. References have been updated and a small number of mistakes have been rectified.
Applications Of Lie Groups To Differential Equations
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Author : Peter J. Olver
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Lie Groups To Differential Equations written by Peter J. Olver and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.
Linear Port Hamiltonian Systems On Infinite Dimensional Spaces
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Author : Birgit Jacob
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-13
Linear Port Hamiltonian Systems On Infinite Dimensional Spaces written by Birgit Jacob and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-13 with Science categories.
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.