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Hyperbolic Equations And Waves
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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 and published by American Mathematical Soc.. This book was released on 2000 with total page 218 pages. 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.
Book Synopsis Hyperbolic Partial Differential Equations by : Peter D. Lax
Download or read book Hyperbolic Partial Differential Equations written by Peter D. Lax and published by American Mathematical Soc.. This book was released on 2006 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses. -- Back cover.
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 Equations and Waves by : Marcel Froissart
Download or read book Hyperbolic Equations and Waves written by Marcel Froissart and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: The success of the 1967 Battelle Rencontres was so much appre ciated by the participants and organizers of this experimental set-up that it was soon decided to go on with the experiment. Mathematicians and physicists had found a very suitable frame to overcome their natural shyness, to get occasionally interested into each others' work, to talk 1968 Rencontres have about it, and eventually to know each other. The been organized with the same idea in mind, and even somewhat enlarged in the following sense: the topic chosen - hyperbolic equations and waves - has proved a cornerstone of physics for more than a century and extends over most fields of contemporary physics. It follows immediately that the wide range of physicists concerned could not be represented by more than a couple of specialists in any single field. Thus, aside from bridging the gap between mathematicians and physicists, the 1968 Recontres provided a rather unique occasion to plug many intra disciplinary gaps among physicists. This made the Rencontres quite unpredictable as to how people would - and could - interact, and created a very stimulating environ ment for an unprecedented intellectual venture. From the outside, it may very well look like a hodge-podge of quite unrelated ideas. But it was much less so at the level of day-to-day discussions and informal gatherings where all slowly acquired a comprehensive synthetic view of the subject.
Book Synopsis Hyperbolic Equations and Waves by : Marcel Froissart
Download or read book Hyperbolic Equations and Waves written by Marcel Froissart and published by . This book was released on 1970 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Trends in the Theory of Hyperbolic Equations by : Michael Reissig
Download or read book New Trends in the Theory of Hyperbolic Equations written by Michael Reissig and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting several developments in the theory of hyperbolic equations, this book's contributions deal with questions of low regularity, critical growth, ill-posedness, decay estimates for solutions of different non-linear hyperbolic models, and introduce new approaches based on microlocal methods.
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 Hyperbolic Partial Differential Equations by : Matthew Witten
Download or read book Hyperbolic Partial Differential Equations written by Matthew Witten and published by Elsevier. This book was released on 2014-05-17 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperbolic Partial Differential Equations, Volume 1: Population, Reactors, Tides and Waves: Theory and Applications covers three general areas of hyperbolic partial differential equation applications. These areas include problems related to the McKendrick/Von Foerster population equations, other hyperbolic form equations, and the numerical solution. This text is composed of 15 chapters and begins with surveys of age specific population interactions, populations models of diffusion, nonlinear age dependent population growth with harvesting, local and global stability for the nonlinear renewal equation in the Von Foerster model, and nonlinear age-dependent population dynamics. The next chapters deal with various applications of hyperbolic partial differential equations to such areas as age-structured fish populations, density dependent growth in a cell colony, boll-weevil-cotton crop modeling, age dependent predation and cannibalism, parasite populations, growth of microorganisms, and stochastic perturbations in the Von Foerster model. These topics are followed by discussions of bifurcation of time periodic solutions of the McKendrick equation; the periodic solution of nonlinear hyperbolic problems; and semigroup theory as applied to nonlinear age dependent population dynamics. Other chapters explore the stability of biochemical reaction tanks, an ADI model for the Laplace tidal equations, the Carleman equation, the nonequilibrium behavior of solids that transport heat by second sound, and the nonlinear hyperbolic partial differential equations and dynamic programming. The final chapters highlight two explicitly numerical applications: a predictor-convex corrector method and the Galerkin approximation in hyperbolic partial differential equations. This book will prove useful to practicing engineers, population researchers, physicists, and mathematicians.
Book Synopsis Finite Volume Methods for Hyperbolic Problems by : Randall J. LeVeque
Download or read book Finite Volume Methods for Hyperbolic Problems written by Randall J. LeVeque and published by Cambridge University Press. This book was released on 2002-08-26 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Book Synopsis Hyperbolic Equations and Waves by : M. Froissart
Download or read book Hyperbolic Equations and Waves written by M. Froissart and published by . This book was released on 1970 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quasilinear Hyperbolic Systems and Waves by : Alan Jeffrey
Download or read book Quasilinear Hyperbolic Systems and Waves written by Alan Jeffrey and published by Pitman Publishing. This book was released on 1976 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The solution to quasilinear first order hyperbolic systems of equations may be interpretated in terms of waves, which belong to a certain function class and propagate in some suitable space, the work all has a common feature the fact that it adds to the understanding of what may be called nonlinear wave propagation" - preface.
Book Synopsis Nonlinear Hyperbolic Waves in Multidimensions by : Phoolan Prasad
Download or read book Nonlinear Hyperbolic Waves in Multidimensions written by Phoolan Prasad and published by CRC Press. This book was released on 2001-05-18 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and pr
Book Synopsis Multi-dimensional Hyperbolic Partial Differential Equations by : Sylvie Benzoni-Gavage
Download or read book Multi-dimensional Hyperbolic Partial Differential Equations written by Sylvie Benzoni-Gavage and published by Oxford University Press, USA. This book was released on 2007 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by leading scholars, this comprehensive text presents a view of the multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. It is useful to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.
Book Synopsis Quasilinear Hyperbolic Systems, Compressible Flows, and Waves by : Vishnu D. Sharma
Download or read book Quasilinear Hyperbolic Systems, Compressible Flows, and Waves written by Vishnu D. Sharma and published by CRC Press. This book was released on 2010-04-29 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. It emphasizes nonlinear theory and introduces some of the most active research in the field.After linking continuum mechanics and quasilinear partial di
Book Synopsis Hyperbolic Equations and Frequency Interactions by : Luis A. Caffarelli
Download or read book Hyperbolic Equations and Frequency Interactions written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on 1999 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research topic for this IAS/PCMS Summer Session was nonlinear wave phenomena. Mathematicians from the more theoretical areas of PDEs were brought together with those involved in applications. The goal was to share ideas, knowledge, and perspectives. How waves, or "frequencies", interact in nonlinear phenomena has been a central issue in many of the recent developments in pure and applied analysis. It is believed that wavelet theory--with its simultaneous localization in both physical and frequency space and its lacunarity--is and will be a fundamental new tool in the treatment of the phenomena. Included in this volume are write-ups of the "general methods and tools" courses held by Jeff Rauch and Ingrid Daubechies. Rauch's article discusses geometric optics as an asymptotic limit of high-frequency phenomena. He shows how nonlinear effects are reflected in the asymptotic theory. In the article "Harmonic Analysis, Wavelets and Applications" by Daubechies and Gilbert the main structure of the wavelet theory is presented. Also included are articles on the more "specialized" courses that were presented, such as "Nonlinear Schrödinger Equations" by Jean Bourgain and "Waves and Transport" by George Papanicolaou and Leonid Ryzhik. Susan Friedlander provides a written version of her lecture series "Stability and Instability of an Ideal Fluid", given at the Mentoring Program for Women in Mathematics, a preliminary program to the Summer Session. This Summer Session brought together students, fellows, and established mathematicians from all over the globe to share ideas in a vibrant and exciting atmosphere. This book presents the compelling results. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Book Synopsis Huygens' Principle and Hyperbolic Equations by : Gunther Paul
Download or read book Huygens' Principle and Hyperbolic Equations written by Gunther Paul and published by Academic Press. This book was released on 2014-07-14 with total page 908 pages. Available in PDF, EPUB and Kindle. Book excerpt: Huygens' Principle and Hyperbolic Equations is devoted to certain mathematical aspects of wave propagation in curved space-times. The book aims to present special nontrivial Huygens' operators and to describe their individual properties and to characterize these examples of Huygens' operators within certain more or less comprehensive classes of general hyperbolic operators. The materials covered in the book include a treatment of the wave equation for p-forms over a space of constant sectional curvature, the Riesz distributions, the Euler-Poisson-Darboux-equations over a Riemannian manifold, and plane wave manifolds. Physicists will find the book invaluable.
Author :Philippe G. LeFloch Publisher :Springer Science & Business Media ISBN 13 :9783764366872 Total Pages :1010 pages Book Rating :4.3/5 (668 download)
Book Synopsis Hyperbolic Systems of Conservation Laws by : Philippe G. LeFloch
Download or read book Hyperbolic Systems of Conservation Laws written by Philippe G. LeFloch and published by Springer Science & Business Media. This book was released on 2002-07-01 with total page 1010 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.
