The Hyperbolic Cauchy Problem
DOWNLOAD
Download The Hyperbolic Cauchy Problem PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Hyperbolic Cauchy Problem book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Hyperbolic Cauchy Problem
DOWNLOAD
Author : Kunihiko Kajitani
language : en
Publisher: Springer
Release Date : 2006-11-15
The Hyperbolic Cauchy Problem written by Kunihiko Kajitani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The approach to the Cauchy problem taken here by the authors is based on theuse of Fourier integral operators with a complex-valued phase function, which is a time function chosen suitably according to the geometry of the multiple characteristics. The correctness of the Cauchy problem in the Gevrey classes for operators with hyperbolic principal part is shown in the first part. In the second part, the correctness of the Cauchy problem for effectively hyperbolic operators is proved with a precise estimate of the loss of derivatives. This method can be applied to other (non) hyperbolic problems. The text is based on a course of lectures given for graduate students but will be of interest to researchers interested in hyperbolic partial differential equations. In the latter part the reader is expected to be familiar with some theory of pseudo-differential operators.
The Hyperbolic Cauchy Problem
DOWNLOAD
Author : Kunihiko Kajitani
language : en
Publisher:
Release Date : 2014-01-15
The Hyperbolic Cauchy Problem written by Kunihiko Kajitani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Cauchy S Problem For Hyperbolic Equations
DOWNLOAD
Author : Lars Gårding
language : en
Publisher:
Release Date : 1958
Cauchy S Problem For Hyperbolic Equations written by Lars Gårding and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Cauchy problem categories.
The Cauchy Problem For Hyperbolic Operators
DOWNLOAD
Author : Karen Yagdjian
language : en
Publisher: De Gruyter Akademie Forschung
Release Date : 1997
The Cauchy Problem For Hyperbolic Operators written by Karen Yagdjian and has been published by De Gruyter Akademie Forschung this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Hyperbolic Partial Differential Equations
DOWNLOAD
Author : Serge Alinhac
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-17
Hyperbolic Partial Differential Equations written by Serge Alinhac and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-17 with Mathematics categories.
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.
Partial Differential Equations In Classical Mathematical Physics
DOWNLOAD
Author : Isaak Rubinstein
language : en
Publisher: Cambridge University Press
Release Date : 1998-04-28
Partial Differential Equations In Classical Mathematical Physics written by Isaak Rubinstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-28 with Mathematics categories.
The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.
Hyperbolic Systems Of Conservation Laws
DOWNLOAD
Author : Alberto Bressan
language : en
Publisher: OUP Oxford
Release Date : 2000
Hyperbolic Systems Of Conservation Laws written by Alberto Bressan and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions, characterized by the appearance of shock waves. This area has experienced substantial progress in very recent years thanks to the introduction of new techniques, in particular the front tracking algorithm and the semigroup approach. These techniques provide a solution to the long standing open problems of uniqueness and stability of entropy weak solutions. This volume is the first to present a comprehensive account of these new, fundamental advances. It also includes a detailed analysis of the stability and convergence of the front tracking algorithm. A set of problems, with varying difficulty is given at the end of each chapter to verify and expand understanding of the concepts and techniques previously discussed. For researchers, this book will provide an indispensable reference to the state of the art in the field of hyperbolic systems of conservation laws.
The Cauchy Problem In Kinetic Theory
DOWNLOAD
Author : Robert T. Glassey
language : en
Publisher: SIAM
Release Date : 1996-01-01
The Cauchy Problem In Kinetic Theory written by Robert T. Glassey and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Science categories.
This volume studies the basic equations of kinetic theory in all of space. It contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations, including the Boltzmann equation (from rarefied gas dynamics) and the Vlasov-Poisson/Vlasov-Maxwell systems (from plasma physics). This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although these equations describe very different phenomena, they share the same streaming term. The author proves that solutions starting from a given configuration at an initial time exist for all future times by imposing appropriate hypotheses on the initial values in several important cases. He emphasizes those questions that a mathematician would ask first: Is there a solution to this problem? Is it unique? Can it be numerically approximated? The topics treated include the study of the Boltzmann collision operator, the study of the initial-value problem for the Boltzmann equation with "small" and "near equilibrium" data, global smooth solvability of the initial-value problem for the Vlasov-Poisson system with smooth initial data of unrestricted size, conditions under which the initial-value problem for the Vlasov-Maxwell system has global-in-time solutions (in both the smooth and weak senses), and more.
Lectures On Cauchy S Problem In Linear Partial Differential Equations
DOWNLOAD
Author : Jacques Hadamard
language : en
Publisher: Courier Corporation
Release Date : 2014-08-25
Lectures On Cauchy S Problem In Linear Partial Differential Equations written by Jacques Hadamard and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-25 with Mathematics categories.
Would well repay study by most theoretical physicists." — Physics Today "An overwhelming influence on subsequent work on the wave equation." — Science Progress "One of the classical treatises on hyperbolic equations." — Royal Naval Scientific Service Delivered at Columbia University and the Universities of Rome and Zürich, these lectures represent a pioneering investigation. Jacques Hadamard based his research on prior studies by Riemann, Kirchhoff, and Volterra. He extended and improved Volterra's work, applying its theories relating to spherical and cylindrical waves to all normal hyperbolic equations instead of only to one. Topics include the general properties of Cauchy's problem, the fundamental formula and the elementary solution, equations with an odd number of independent variables, and equations with an even number of independent variables and the method of descent.
Hyperbolic Differential Operators And Related Problems
DOWNLOAD
Author : Vincenzo Ancona
language : en
Publisher: CRC Press
Release Date : 2003-03-06
Hyperbolic Differential Operators And Related Problems written by Vincenzo Ancona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-06 with Mathematics categories.
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.