Lecture Notes On Geometrical Aspects Of Partial Differential Equations

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Lecture Notes on Geometrical Aspects of Partial Differential Equations

V V Zharinov
Lecture Notes on Geometrical Aspects of Partial Differential Equations Book PDF

Author : V V Zharinov
Publisher : World Scientific
Page : 372 pages
File Size : 41,7 Mb
Release : 1992-03-26
Category : Mathematics
ISBN : 9789814513999

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Lecture Notes on Geometrical Aspects of Partial Differential Equations by V V Zharinov Pdf

This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text. Contents:Introduction: Internal Geometry of PDE:Differential ManifoldsLie-Backlund MappingsLie-Backlund Fields and Infinitesimal SymmetriesCartan Forms, Currents and Conservation LawsC-Spectral Sequence. Further Properties of Conservation LawsTrivial Equations. The Formal Variational CalculusEvolution EquationsExternal Geometry of PDE:Differential SubmanifoldsNormal Projection. External Fields and FormsTrivial Ambient Differential ManifoldsThe Characteristic MappingThe Green's FormulaLow-Dimensional Conservation LawsBacklund CorrespondenceFurther Studies:Lagrangian FormalismHamiltonian EquationsExample: The Nambu's StringAppendix Readership: Graduate students and researchers in mathematical physics. keywords:Differential Manifolds;Lie-Bäcklund Mappings;Cartan Forms;Currents;Conservation Laws;Lagrangian Formation;Hamiltonian Equations

Lecture Notes on Geometrical Aspects of Partial Differential Equations

Viktor Viktorovich Zharinov
Lecture Notes on Geometrical Aspects of Partial Differential Equations Book PDF

Author : Viktor Viktorovich Zharinov
Publisher : World Scientific
Page : 380 pages
File Size : 43,5 Mb
Release : 1992
Category : Mathematics
ISBN : 9810207530

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Lecture Notes on Geometrical Aspects of Partial Differential Equations by Viktor Viktorovich Zharinov Pdf

This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text.

Analytic, Algebraic and Geometric Aspects of Differential Equations

Galina Filipuk,Yoshishige Haraoka,Sławomir Michalik
Analytic Algebraic and Geometric Aspects of Differential Equations Book PDF

Author : Galina Filipuk,Yoshishige Haraoka,Sławomir Michalik
Publisher : Birkhäuser
Page : 471 pages
File Size : 48,5 Mb
Release : 2017-06-23
Category : Mathematics
ISBN : 9783319528427

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Analytic, Algebraic and Geometric Aspects of Differential Equations by Galina Filipuk,Yoshishige Haraoka,Sławomir Michalik Pdf

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.

Nonlinear partial differential equations in differential geometry

Robert Hardt
Nonlinear partial differential equations in differential geometry Book PDF

Author : Robert Hardt
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 52,7 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.

Geometric Analysis and PDEs

Matthew J. Gursky,Ermanno Lanconelli,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang
Geometric Analysis and PDEs Book PDF

Author : Matthew J. Gursky,Ermanno Lanconelli,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 50,7 Mb
Release : 2009-06-26
Category : Mathematics
ISBN : 9783642016738

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Geometric Analysis and PDEs by Matthew J. Gursky,Ermanno Lanconelli,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang Pdf

This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.

Geometric Aspects of Partial Differential Equations

Bernhelm Booss,Krzysztof Wojciechowski,Krzysztof P. Wojciechowski
Geometric Aspects of Partial Differential Equations Book PDF

Author : Bernhelm Booss,Krzysztof Wojciechowski,Krzysztof P. Wojciechowski
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 47,6 Mb
Release : 1999
Category : Geometry, Differential
ISBN : 9780821820612

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Geometric Aspects of Partial Differential Equations by Bernhelm Booss,Krzysztof Wojciechowski,Krzysztof P. Wojciechowski Pdf

This collection of papers by leading researchers gives a broad picture of current research directions in geometric aspects of partial differential equations. Based on lectures presented at a Minisymposium on Spectral Invariants - Heat Equation Approach, held in September 1998 at Roskilde University in Denmark, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are new index theorems as well as new calculations of the eta-invariant, of the spectral flow, of the Maslov index, of Seiberg-Witten monopoles, heat kernels, determinants, non-commutative residues, and of the Ray-Singer torsion. New types of boundary value problems for operators of Dirac type and generalizations to manifolds with cuspidal ends, to non-compact and to infinite-dimensional manifolds are also discussed. Throughout the book, the use of advanced analysis methods for gaining geometric insight emerges as a central theme. Aimed at graduate students and researchers, this book would be suitable as a text for an advanced graduate topics course on geometric aspects of partial differential equations and spectral invariants.

Partial Differential Equations and Geometric Measure Theory

Alessio Figalli,Enrico Valdinoci,Ireneo Peral
Partial Differential Equations and Geometric Measure Theory Book PDF

Author : Alessio Figalli,Enrico Valdinoci,Ireneo Peral
Publisher : Springer
Page : 216 pages
File Size : 42,8 Mb
Release : 2018-05-23
Category : Mathematics
ISBN : 9783319740423

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Partial Differential Equations and Geometric Measure Theory by Alessio Figalli,Enrico Valdinoci,Ireneo Peral Pdf

This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.

Geometric Analysis and PDEs

Matthew J. Gursky,Ermanno Lanconelli,Andrea Malchiodi,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang
Geometric Analysis and PDEs Book PDF

Author : Matthew J. Gursky,Ermanno Lanconelli,Andrea Malchiodi,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang
Publisher : Springer
Page : 256 pages
File Size : 46,5 Mb
Release : 2009-08-29
Category : Mathematics
ISBN : 3642016758

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Geometric Analysis and PDEs by Matthew J. Gursky,Ermanno Lanconelli,Andrea Malchiodi,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang Pdf

This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.

Quantization, PDEs, and Geometry

Dorothea Bahns,Wolfram Bauer,Ingo Witt
Quantization PDEs and Geometry Book PDF

Author : Dorothea Bahns,Wolfram Bauer,Ingo Witt
Publisher : Birkhäuser
Page : 314 pages
File Size : 41,9 Mb
Release : 2016-02-11
Category : Mathematics
ISBN : 9783319224077

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Quantization, PDEs, and Geometry by Dorothea Bahns,Wolfram Bauer,Ingo Witt Pdf

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.

Geometry of PDEs and Related Problems

Xavier Cabré,Antoine Henrot,Daniel Peralta-Salas,Wolfgang Reichel,Henrik Shahgholian
Geometry of PDEs and Related Problems Book PDF

Author : Xavier Cabré,Antoine Henrot,Daniel Peralta-Salas,Wolfgang Reichel,Henrik Shahgholian
Publisher : Springer
Page : 198 pages
File Size : 50,6 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9783319951867

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Geometry of PDEs and Related Problems by Xavier Cabré,Antoine Henrot,Daniel Peralta-Salas,Wolfgang Reichel,Henrik Shahgholian Pdf

The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date references. Collecting together the lecture notes of the five mini-courses given at the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19–23, 2017, the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details on the main ideas of the proofs, their technical difficulties, and their possible extension to other contexts. Aiming to be a primary source for researchers in the field, the book will attract potential readers from several areas of mathematics.

Nonlinear PDEs, Their Geometry, and Applications

Radosław A. Kycia,Maria Ułan,Eivind Schneider
Nonlinear PDEs Their Geometry and Applications Book PDF

Author : Radosław A. Kycia,Maria Ułan,Eivind Schneider
Publisher : Springer
Page : 279 pages
File Size : 53,7 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.

Differential Geometry, Differential Equations, and Mathematical Physics

Maria Ulan,Eivind Schneider
Differential Geometry Differential Equations and Mathematical Physics Book PDF

Author : Maria Ulan,Eivind Schneider
Publisher : Birkhäuser
Page : 231 pages
File Size : 42,7 Mb
Release : 2022-02-13
Category : Mathematics
ISBN : 3030632555

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Differential Geometry, Differential Equations, and Mathematical Physics by Maria Ulan,Eivind Schneider Pdf

This volume presents lectures given at the Wisła 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations, and are included here as lecture notes comprising the first three chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and mathematical physics. Specific topics covered include: Parabolic geometry Geometric methods for solving PDEs in physics, mathematical biology, and mathematical finance Darcy and Euler flows of real gases Differential invariants for fluid and gas flow Differential Geometry, Differential Equations, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry is assumed.

Geometry in Partial Differential Equations

Agostino Prastaro,Themistocles M. Rassias
Geometry in Partial Differential Equations Book PDF

Author : Agostino Prastaro,Themistocles M. Rassias
Publisher : World Scientific
Page : 482 pages
File Size : 44,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9810214073

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Geometry in Partial Differential Equations by Agostino Prastaro,Themistocles M. Rassias Pdf

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.

Elliptic–Hyperbolic Partial Differential Equations

Thomas H. Otway
Elliptic Hyperbolic Partial Differential Equations Book PDF

Author : Thomas H. Otway
Publisher : Springer
Page : 128 pages
File Size : 46,8 Mb
Release : 2015-07-08
Category : Mathematics
ISBN : 9783319197616

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Elliptic–Hyperbolic Partial Differential Equations by Thomas H. Otway Pdf

This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.

Partial Differential Equations

Walter A. Strauss
Partial Differential Equations Book PDF

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 41,5 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

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Partial Differential Equations by Walter A. Strauss Pdf

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.