Cauchy S Problem For Hyperbolic Equations
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Cauchy S Problem For Hyperbolic Equations
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Author : Lars Gårding
language : en
Publisher:
Release Date : 1957
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 1957 with Differential equations, Partial categories.
Partial Differential Equations In Classical Mathematical Physics
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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.
Lectures On Cauchy S Problem In Linear Partial Differential Equations
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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 Partial Differential Equations
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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.
The Cauchy Problem For Hyperbolic Operators
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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.
Einstein S Field Equations And Their Physical Implications
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Author : Bernd G. Schmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-02-18
Einstein S Field Equations And Their Physical Implications written by Bernd G. Schmidt 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 2000-02-18 with Mathematics categories.
This book serves two purposes. The authors present important aspects of modern research on the mathematical structure of Einstein's field equations and they show how to extract their physical content from them by mathematically exact methods. The essays are devoted to exact solutions and to the Cauchy problem of the field equations as well as to post-Newtonian approximations that have direct physical implications. Further topics concern quantum gravity and optics in gravitational fields. The book addresses researchers in relativity and differential geometry but can also be used as additional reading material for graduate students.
Finite Difference Methods For Ordinary And Partial Differential Equations
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Author : Randall J. LeVeque
language : en
Publisher: SIAM
Release Date : 2007-01-01
Finite Difference Methods For Ordinary And Partial Differential Equations written by Randall J. LeVeque and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Hyperbolic Equations And Related Topics
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Author : Sigeru Mizohata
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Hyperbolic Equations And Related Topics written by Sigeru Mizohata and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Hyperbolic Equations and Related Topics covers the proceedings of the Taniguchi International Symposium, held in Katata, Japan on August 27-31, 1984 and in Kyoto, Japan on September 3-5, 1984. The book focuses on the mathematical analyses involved in hyperbolic equations. The selection first elaborates on complex vector fields; holomorphic extension of CR functions and related problems; second microlocalization and propagation of singularities for semi-linear hyperbolic equations; and scattering matrix for two convex obstacles. Discussions focus on the construction of asymptotic solutions, singular vector fields and Leibniz formula, second microlocalization along a Lagrangean submanifold, and hypo-analytic structures. The text then ponders on the Cauchy problem for effectively hyperbolic equations and for uniformly diagonalizable hyperbolic systems in Gevrey classes. The book takes a look at generalized Hamilton flows and singularities of solutions of the hyperbolic Cauchy problem and analytic and Gevrey well-posedness of the Cauchy problem for second order weakly hyperbolic equations with coefficients irregular in time. The selection is a dependable reference for researchers interested in hyperbolic equations.
Uniqueness Problems For Degenerating Equations And Nonclassical Problems
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Author : S. P. Shishatskii
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-10-15
Uniqueness Problems For Degenerating Equations And Nonclassical Problems written by S. P. Shishatskii and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-15 with Mathematics categories.
No detailed description available for "Uniqueness Problems for Degenerating Equations and Nonclassical Problems".
Initial Boundary Value Problems And The Navier Stokes Equation
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Author : Heinz-Otto Kreiss
language : en
Publisher: SIAM
Release Date : 2004-01-01
Initial Boundary Value Problems And The Navier Stokes Equation written by Heinz-Otto Kreiss and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Science categories.
Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. Audience: when the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplifications have been used throughout. This book continues to be useful to researchers and graduate students in applied mathematics and engineering.