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Geometric Analysis of Hyperbolic Differential Equations: An Introduction

2010-05-20 Mathematics
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Release : 2010-05-20
Genre : Mathematics
Kind : eBook
Book Rating : 814/5 ( reviews)

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Book Synopsis Geometric Analysis of Hyperbolic Differential Equations: An Introduction by : S. Alinhac

Download or read book Geometric Analysis of Hyperbolic Differential Equations: An Introduction written by S. Alinhac. This book was released on 2010-05-20. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Analysis of Hyperbolic Differential Equations

2010 Differential equations, Hyperbolic
Download Geometric Analysis of Hyperbolic Differential Equations PDF Online Free

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Release : 2010
Genre : Differential equations, Hyperbolic
Kind : eBook
Book Rating : 587/5 ( reviews)

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Book Synopsis Geometric Analysis of Hyperbolic Differential Equations by : Serge Alinhac

Download or read book Geometric Analysis of Hyperbolic Differential Equations written by Serge Alinhac. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: "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"--Provided by publisher.

Geometric Analysis and Nonlinear Partial Differential Equations

2003 Mathematics
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Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 512/5 ( reviews)

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Book Synopsis Geometric Analysis and Nonlinear Partial Differential Equations by : Stefan Hildebrandt

Download or read book Geometric Analysis and Nonlinear Partial Differential Equations written by Stefan Hildebrandt. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: This well-organized and coherent collection of papers leads the reader to the frontiers of present research in the theory of nonlinear partial differential equations and the calculus of variations and offers insight into some exciting developments. In addition, most articles also provide an excellent introduction to their background, describing extensively as they do the history of those problems presented, as well as the state of the art and offer a well-chosen guide to the literature. Part I contains the contributions of geometric nature: From spectral theory on regular and singular spaces to regularity theory of solutions of variational problems. Part II consists of articles on partial differential equations which originate from problems in physics, biology and stochastics. They cover elliptic, hyperbolic and parabolic cases.

Hyperbolic Partial Differential Equations and Wave Phenomena

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 217/5 ( reviews)

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Book Synopsis Hyperbolic Partial Differential Equations and Wave Phenomena by : Mitsuru Ikawa

Download or read book Hyperbolic Partial Differential Equations and Wave Phenomena written by Mitsuru Ikawa. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: The familiar wave equation is the most fundamental hyperbolic partial differential equation. Other hyperbolic equations, both linear and nonlinear, exhibit many wave-like phenomena. The primary theme of this book is the mathematical investigation of such wave phenomena. The exposition begins with derivations of some wave equations, including waves in an elastic body, such as those observed in connection with earthquakes. Certain existence results are proved early on, allowing the later analysis to concentrate on properties of solutions. The existence of solutions is established using methods from functional analysis. Many of the properties are developed using methods of asymptotic solutions. The last chapter contains an analysis of the decay of the local energy of solutions. This analysis shows, in particular, that in a connected exterior domain, disturbances gradually drift into the distance and the effect of a disturbance in a bounded domain becomes small after sufficient time passes. The book is geared toward a wide audience interested in PDEs. Prerequisite to the text are some real analysis and elementary functional analysis. It would be suitable for use as a text in PDEs or mathematical physics at the advanced undergraduate and graduate level.

Hyperbolic Partial Differential Equations and Geometric Optics

2012-05-01 Mathematics
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Release : 2012-05-01
Genre : Mathematics
Kind : eBook
Book Rating : 915/5 ( reviews)

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Book Synopsis Hyperbolic Partial Differential Equations and Geometric Optics by : Jeffrey Rauch

Download or read book Hyperbolic Partial Differential Equations and Geometric Optics written by Jeffrey Rauch. This book was released on 2012-05-01. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations. One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader. The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics.

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