Geometric Analysis Of Hyperbolic Differential Equations An Introduction
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| Author | : S. Alinhac |
| Publisher | : Cambridge University Press |
| Total Pages | : |
| Release | : 2010-05-20 |
| Genre | : Mathematics |
| ISBN | : 1139485814 |
Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required.
| Author | : Serge Alinhac |
| Publisher | : |
| Total Pages | : 129 |
| Release | : 2014-05-14 |
| Genre | : Differential equations, Hyperbolic |
| ISBN | : 9781139127844 |
A self-contained presentation of the tools of Lorentzian geometry necessary to access recent works in mathematical relativity.
| Author | : Walter A. Strauss |
| Publisher | : John Wiley & Sons |
| Total Pages | : 467 |
| Release | : 2007-12-21 |
| Genre | : Mathematics |
| ISBN | : 0470054565 |
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.
| Author | : Ovidiu Calin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 285 |
| Release | : 2006-03-15 |
| Genre | : Mathematics |
| ISBN | : 0817644210 |
* A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics
| Author | : Serge Alinhac |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 159 |
| Release | : 2009-06-17 |
| Genre | : Mathematics |
| ISBN | : 0387878238 |
This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over 100 exercises are included, as well as "do it yourself" instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher.
| Author | : Anthony G. O'Farrell |
| Publisher | : Cambridge University Press |
| Total Pages | : 295 |
| Release | : 2015-05-28 |
| Genre | : Mathematics |
| ISBN | : 1107442885 |
An accessible yet systematic account of reversibility that demonstrates its impact throughout many diverse areas of mathematics.
| Author | : David B. Ellis |
| Publisher | : Cambridge University Press |
| Total Pages | : 283 |
| Release | : 2014-06-05 |
| Genre | : Mathematics |
| ISBN | : 1139952935 |
Focusing on the role that automorphisms and equivalence relations play in the algebraic theory of minimal sets provides an original treatment of some key aspects of abstract topological dynamics. Such an approach is presented in this lucid and self-contained book, leading to simpler proofs of classical results, as well as providing motivation for further study. Minimal flows on compact Hausdorff spaces are studied as icers on the universal minimal flow M. The group of the icer representing a minimal flow is defined as a subgroup of the automorphism group G of M, and icers are constructed explicitly as relative products using subgroups of G. Many classical results are then obtained by examining the structure of the icers on M, including a proof of the Furstenberg structure theorem for distal extensions. This book is designed as both a guide for graduate students, and a source of interesting new ideas for researchers.
| Author | : Mark Hagen |
| Publisher | : Cambridge University Press |
| Total Pages | : 242 |
| Release | : 2019-07-11 |
| Genre | : Mathematics |
| ISBN | : 1108577350 |
Since the notion was introduced by Gromov in the 1980s, hyperbolicity of groups and spaces has played a significant role in geometric group theory; hyperbolic groups have good geometric properties that allow us to prove strong results. However, many classes of interest in our exploration of the universe of finitely generated groups contain examples that are not hyperbolic. Thus we wish to go 'beyond hyperbolicity' to find good generalisations that nevertheless permit similarly strong results. This book is the ideal resource for researchers wishing to contribute to this rich and active field. The first two parts are devoted to mini-courses and expository articles on coarse median spaces, semihyperbolicity, acylindrical hyperbolicity, Morse boundaries, and hierarchical hyperbolicity. These serve as an introduction for students and a reference for experts. The topics of the surveys (and more) re-appear in the research articles that make up Part III, presenting the latest results beyond hyperbolicity.
| Author | : Leticia Brambila |
| Publisher | : Cambridge University Press |
| Total Pages | : 347 |
| Release | : 2014-03-13 |
| Genre | : Mathematics |
| ISBN | : 1107636388 |
A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.
| Author | : Yann Ollivier |
| Publisher | : Cambridge University Press |
| Total Pages | : 317 |
| Release | : 2014-08-07 |
| Genre | : Mathematics |
| ISBN | : 1139993623 |
The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimension conditions, and traffic congestion.
