Nonlinear Partial Differential Equations In Geometry And Physics

Author : Garth Baker,Alexandre Freire
Publisher : Birkhäuser
Page : 166 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034888950

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Nonlinear Partial Differential Equations in Geometry and Physics by Garth Baker,Alexandre Freire Pdf

This volume presents the proceedings of a series of lectures hosted by the Math ematics Department of The University of Tennessee, Knoxville, March 22-24, 1995, under the title "Nonlinear Partial Differential Equations in Geometry and Physics" . While the relevance of partial differential equations to problems in differen tial geometry has been recognized since the early days of the latter subject, the idea that differential equations of differential-geometric origin can be useful in the formulation of physical theories is a much more recent one. Perhaps the earliest emergence of systems of nonlinear partial differential equations having deep geo metric and physical importance were the Einstein equations of general relativity (1915). Several basic aspects of the initial value problem for the Einstein equa tions, such as existence, regularity and stability of solutions remain prime research areas today. eighty years after Einstein's work. An even more recent development is the realization that structures originally the context of models in theoretical physics may turn out to have introduced in important geometric or topological applications. Perhaps its emergence can be traced back to 1954, with the introduction of a non-abelian version of Maxwell's equations as a model in elementary-particle physics, by the physicists C.N. Yang and R. Mills. The rich geometric structure ofthe Yang-Mills equations was brought to the attention of mathematicians through work of M.F. Atiyah, :"J. Hitchin, I.

Author : Garth Baker,Alexandre S. Freire
Publisher : Birkhauser
Page : 153 pages
File Size : 51,6 Mb
Release : 1997-01-01
Category : Differential equations, Nonlinear
ISBN : 0817654933

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Nonlinear Partial Differential Equations in Geometry and Physics by Garth Baker,Alexandre S. Freire Pdf

This volume contains survey lectures in four different areas, delivered by leading researchers at the 1995 Barrett Lectures held at the University of Tennessee: nonlinear hyperbolic systems arising in field theory and relativity (S. Klainerman); harmonic maps from Minkowski spacetime (M. Struwe); dynamics of vortices in the Ginzburg-Landau model of superconductivity (F.-H. Lin); the Seiberg-Witten equations and their application to problems in four-dimensional topology (R. Fintushel). Most of this material has not previously been available in survey form. These lectures provide an up-to-date overview and an introduction to the research literature in each of these areas, which should prove useful to researchers and graduate students in mathematical physics, partial differential equations, differential geometry and topology.

Author : Radosław A. Kycia,Maria Ułan,Eivind Schneider
Publisher : Springer
Page : 279 pages
File Size : 40,7 Mb
Release : 2019-05-18
Category : Mathematics
ISBN : 9783030170318

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Nonlinear PDEs, Their Geometry, and Applications by Radosław A. Kycia,Maria Ułan,Eivind Schneider Pdf

This volume presents lectures given at the Summer School Wisła 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part of this volume were delivered by experts in nonlinear differential equations and their applications to physics. Original research articles from members of the school comprise the second part of this volume. Much of the latter half of the volume complements the methods expounded in the first half by illustrating additional applications of geometric theory of differential equations. Various subjects are covered, providing readers a glimpse of current research. Other topics covered include thermodynamics, meteorology, and the Monge–Ampère equations. Researchers interested in the applications of nonlinear differential equations to physics will find this volume particularly useful. A knowledge of differential geometry is recommended for the first portion of the book, as well as a familiarity with basic concepts in physics.

Author : Vladimir Oliker,Andrejs Treibergs,American Mathematical Society. Meeting
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 48,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821851357

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Geometry and Nonlinear Partial Differential Equations by Vladimir Oliker,Andrejs Treibergs,American Mathematical Society. Meeting Pdf

This volume contains the proceedings of an AMS Special Session on Geometry, Physics, and Nonlinear PDEs, held in March 1990 at the AMS meeting in Fayetteville. In recent years, there has been an enormous surge of activity in these areas, and there was an overwhelming response to invitations to the session. The conference brought together specialists in Monge-Ampere equations, prescribed curvature problems, mean curvature, harmonic maps, evolution with curvature-dependent speed, isospectral manifolds, and general relativity. Twenty-five half-hour addresses were presented at the session, and the majority of the papers in this volume are expositions of those addresses. The book provides an excellent overview of the frontiers of research in these areas.

Author : P.A. Clarkson
Publisher : Springer Science & Business Media
Page : 466 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401120821

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Applications of Analytic and Geometric Methods to Nonlinear Differential Equations by P.A. Clarkson Pdf

In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.

Author : Shing-Tung Yau,Shuxing Chen
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 49,8 Mb
Release : 2002
Category : Differential equations, Nonlinear
ISBN : 9780821832943

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Geometry and Nonlinear Partial Differential Equations by Shing-Tung Yau,Shuxing Chen Pdf

This book presents the proceedings of a conference on geometry and nonlinear partial differential equations dedicated to Professor Buqing Su in honor of his one-hundredth birthday. It offers a look at current research by Chinese mathematicians in differential geometry and geometric areas of mathematical physics. It is suitable for advanced graduate students and research mathematicians interested in geometry, topology, differential equations, and mathematical physics.

Author : Robert Hardt
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 53,9 Mb
Release : 1996
Category : Mathematics
ISBN : 0821804316

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Nonlinear partial differential equations in differential geometry by Robert Hardt Pdf

This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.

Author : Victor A. Galaktionov,Sergey R. Svirshchevskii
Publisher : CRC Press
Page : 538 pages
File Size : 47,9 Mb
Release : 2006-11-02
Category : Mathematics
ISBN : 1584886633

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Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics by Victor A. Galaktionov,Sergey R. Svirshchevskii Pdf

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.

Author : Luis A. Caffarelli,François Golse,Yan Guo,Carlos E. Kenig,Alexis Vasseur
Publisher : Springer Science & Business Media
Page : 150 pages
File Size : 48,5 Mb
Release : 2012-02-02
Category : Mathematics
ISBN : 9783034801911

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Nonlinear Partial Differential Equations by Luis A. Caffarelli,François Golse,Yan Guo,Carlos E. Kenig,Alexis Vasseur Pdf

The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and wave equations. The book describes in a careful and expository manner several powerful methods from recent top research articles.

Author : Mohamed Ben Ayed,Mohamed Ali Jendoubi,Yomna Rébaï,Hasna Riahi,Hatem Zaag
Publisher : Cambridge University Press
Page : 471 pages
File Size : 41,8 Mb
Release : 2019-05-02
Category : Mathematics
ISBN : 9781108431637

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Partial Differential Equations arising from Physics and Geometry by Mohamed Ben Ayed,Mohamed Ali Jendoubi,Yomna Rébaï,Hasna Riahi,Hatem Zaag Pdf

Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.

Author : Stefan Hildebrandt,Hermann Karcher
Publisher : Springer Science & Business Media
Page : 663 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642556272

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Geometric Analysis and Nonlinear Partial Differential Equations by Stefan Hildebrandt,Hermann Karcher Pdf

This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.

Author : Iosif Semenovich Krasilʹshchik,Valentin Vasilʹevich Lychagin,Aleksandr Mikhaĭlovich Vinogradov
Publisher : Routledge
Page : 472 pages
File Size : 49,8 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39015015702395

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Geometry of Jet Spaces and Nonlinear Partial Differential Equations by Iosif Semenovich Krasilʹshchik,Valentin Vasilʹevich Lychagin,Aleksandr Mikhaĭlovich Vinogradov Pdf

Author : Lokenath Debnath
Publisher : Springer Science & Business Media
Page : 602 pages
File Size : 52,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489928467

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Nonlinear Partial Differential Equations for Scientists and Engineers by Lokenath Debnath Pdf

This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, help make the book more useful for a diverse readership. The book is an exceptionally complete text/reference for graduates, researchers, and professionals in mathematics, physics, and engineering.

Author : Shing-Tung Yau,Institute for Advanced Study (Princeton, N.J.)
Publisher : Princeton University Press
Page : 720 pages
File Size : 55,7 Mb
Release : 1982-03-21
Category : Mathematics
ISBN : 9780691082967

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Seminar on Differential Geometry by Shing-Tung Yau,Institute for Advanced Study (Princeton, N.J.) Pdf

This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential geometry and partial differential equations include a general survey article by the editor on the relationship of the two fields and more specialized articles on topics including harmonic mappings, isoperimetric and Poincaré inequalities, metrics with specified curvature properties, the Monge-Arnpere equation, L2 harmonic forms and cohomology, manifolds of positive curvature, isometric embedding, and Kraumlhler manifolds and metrics. The articles on differential geometry and mathematical physics cover such topics as renormalization, instantons, gauge fields and the Yang-Mills equation, nonlinear evolution equations, incompleteness of space-times, black holes, and quantum gravity. A feature of special interest is the inclusion of a list of more than one hundred unsolved research problems compiled by the editor with comments and bibliographical information.

Author : Michael E. Taylor
Publisher : Springer Nature
Page : 774 pages
File Size : 41,7 Mb
Release : 2023-12-06
Category : Mathematics
ISBN : 9783031339288

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Partial Differential Equations III by Michael E. Taylor Pdf

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L^p Sobolev spaces, Holder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (Peter Lax, SIAM review, June 1998)