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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.

Identification Problems of Wave Phenomena

1999-12 Architecture
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Release : 1999-12
Genre : Architecture
Kind : eBook
Book Rating : 980/5 ( reviews)

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Book Synopsis Identification Problems of Wave Phenomena by : A. Lorenzi

Download or read book Identification Problems of Wave Phenomena written by A. Lorenzi. This book was released on 1999-12. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Hyperbolic Problems

2012 Mathematics
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Release : 2012
Genre : Mathematics
Kind : eBook
Book Rating : 068/5 ( reviews)

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Book Synopsis Hyperbolic Problems by : Song Jiang

Download or read book Hyperbolic Problems written by Song Jiang. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for mathematicians, researchers in applied sciences and graduate students, this book is devoted to mathematical theory, numerics and applications of hyperbolic problems. It covers a range of topics addressing theoretical, modeling and computational issues arising under the umbrella of "Hyperbolic Partial Differential Equations".

Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena

2010-10-01 Mathematics
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Release : 2010-10-01
Genre : Mathematics
Kind : eBook
Book Rating : 76X/5 ( reviews)

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Book Synopsis Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena by : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations

Download or read book Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena written by Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations. This book was released on 2010-10-01. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.

Hyperbolic Partial Differential Equations

2006 Mathematics
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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 769/5 ( reviews)

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Book Synopsis Hyperbolic Partial Differential Equations by : Peter D. Lax

Download or read book Hyperbolic Partial Differential Equations written by Peter D. Lax. This book was released on 2006. 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.

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