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Geometric Analysis Of Hyperbolic Differential Equations An Introduction
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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 and published by Cambridge University Press. This book was released on 2010-05-20 with total page pages. 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.
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 and published by . This book was released on 2014-05-14 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained presentation of the tools of Lorentzian geometry necessary to access recent works in mathematical relativity.
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 and published by Springer Science & Business Media. This book was released on 2003 with total page 696 pages. 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.
Book Synopsis Elliptic–Hyperbolic Partial Differential Equations by : Thomas H. Otway
Download or read book Elliptic–Hyperbolic Partial Differential Equations written by Thomas H. Otway and published by Springer. This book was released on 2015-07-08 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 and published by American Mathematical Soc.. This book was released on 2012-05-01 with total page 386 pages. 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.
Book Synopsis Geometric Analysis and Nonlinear Partial Differential Equations by : Ilya J. Bakelman
Download or read book Geometric Analysis and Nonlinear Partial Differential Equations written by Ilya J. Bakelman and published by CRC Press. This book was released on 1993-02-17 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference features papers from the Special Session of the American Mathematical Society Meeting held in 1990 at the University of North Texas, Denton - discussing and developing research on boundary value problems for nonlinear partial differential equations and related problems.;Written by more than 15 authorities in the field, Geometric Analysis and Nonlinear Partial Differential Equations: presents methods and results of the convex bodies and geometric inequalities theory and its applications to differential equations, geometry, and mathematical physics; details recent studies on Monge-Ampere equations, emphasizing geometric inequalities governing a priori estimates of solutions and existence theorems of the Dirichlet problem for convex generalized solutions and showing the proofs of all theorems; examines the generalization of the isoperimetric inequality for two-dimensional general convex surfaces whose integral Gaussian curvature is less than 2 pi; and contains open problems on the theory of surfaces with constant mean curvature.;Geometric Analysis and Nonlinear Partial Differential Equations is for mathematical analysts, geometers, pure and applied mathematicians, physicists, engineers, computer scientists, and upper-level undergraduate and graduate students in these disciplines.
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 and published by American Mathematical Soc.. This book was released on 2012-01-01 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Partial Differential Equations by : Walter A. Strauss
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Hyperbolic Dynamics and Brownian Motion by : Jacques Franchi
Download or read book Hyperbolic Dynamics and Brownian Motion written by Jacques Franchi and published by Oxford University Press. This book was released on 2012-08-16 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperbolic Dynamics and Brownian Motion illustrates the interplay between distinct domains of mathematics. There is no assumption that the reader is a specialist in any of these domains: only basic knowledge of linear algebra, calculus and probability theory is required. The content can be summarized in three ways: Firstly, this book provides an introduction to hyperbolic geometry, based on the Lorentz group. The Lorentz group plays, in relativistic space-time, a role analogue to the rotations in Euclidean space. The hyperbolic geometry is the geometry of the unit pseudo-sphere. The boundary of the hyperbolic space is defined as the set of light rays. Special attention is given to the geodesic and horocyclic flows. Hyperbolic geometry is presented via special relativity to benefit from the physical intuition. Secondly, this book introduces basic notions of stochastic analysis: the Wiener process, Itô's stochastic integral, and calculus. This introduction allows study in linear stochastic differential equations on groups of matrices. In this way the spherical and hyperbolic Brownian motions, diffusions on the stable leaves, and the relativistic diffusion are constructed. Thirdly, quotients of the hyperbolic space under a discrete group of isometries are introduced. In this framework some elements of hyperbolic dynamics are presented, as the ergodicity of the geodesic and horocyclic flows. This book culminates with an analysis of the chaotic behaviour of the geodesic flow, performed using stochastic analysis methods. This main result is known as Sinai's central limit theorem.
Book Synopsis Hyperbolic Problems and Regularity Questions by : Mariarosaria Padula
Download or read book Hyperbolic Problems and Regularity Questions written by Mariarosaria Padula and published by Springer Science & Business Media. This book was released on 2007-01-21 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics. The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.
Book Synopsis Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology by : Jens Bölte
Download or read book Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology written by Jens Bölte and published by Cambridge University Press. This book was released on 2012 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts introduce this classical subject with exciting new applications in theoretical physics.
Book Synopsis Partial Differential Equations arising from Physics and Geometry by : Mohamed Ben Ayed
Download or read book Partial Differential Equations arising from Physics and Geometry written by Mohamed Ben Ayed and published by Cambridge University Press. This book was released on 2019-05-02 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.
Book Synopsis Hyperbolic Partial Differential Equations by : Serge Alinhac
Download or read book Hyperbolic Partial Differential Equations written by Serge Alinhac and published by Springer Science & Business Media. This book was released on 2009-06-17 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Hyperbolic Differential Operators And Related Problems by : Vincenzo Ancona
Download or read book Hyperbolic Differential Operators And Related Problems written by Vincenzo Ancona and published by CRC Press. This book was released on 2003-03-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the topic, this text is key for researchers and mathematicians specializing in hyperbolic, Schrödinger, Einstein, and partial differential equations; complex analysis; and mathematical physics.
Book Synopsis Partial Differential Equations by : Jürgen Jost
Download or read book Partial Differential Equations written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2010-04-30 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. It also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. It also explores connections between elliptic, parabolic, and hyperbolic equations as well as the connection with Brownian motion and semigroups. This second edition features a new chapter on reaction-diffusion equations and systems.
Book Synopsis Analysis and Geometry on Graphs and Manifolds by : Matthias Keller
Download or read book Analysis and Geometry on Graphs and Manifolds written by Matthias Keller and published by Cambridge University Press. This book was released on 2020-08-20 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: A contemporary exploration of the interplay between geometry, spectral theory and stochastics which is explored for graphs and manifolds.
Book Synopsis Stochastic Stability of Differential Equations in Abstract Spaces by : Kai Liu
Download or read book Stochastic Stability of Differential Equations in Abstract Spaces written by Kai Liu and published by Cambridge University Press. This book was released on 2019-05-02 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a unified treatment of stochastic differential equations in abstract, mainly Hilbert, spaces.
