Softcover ISBN:  9780821810217 
Product Code:  MMONO/189 
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AMS Member Price:  $38.40 
Electronic ISBN:  9781470446031 
Product Code:  MMONO/189.E 
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Book DetailsTranslations of Mathematical MonographsIwanami Series in Modern MathematicsVolume: 189; 2000; 190 ppMSC: Primary 35;
The familiar wave equation is the most fundamental hyperbolic partial differential equation. Other hyperbolic equations, both linear and nonlinear, exhibit many wavelike 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.ReadershipAdvanced undergraduate and graduate students and researchers interested in partial differential equations and mathematical physics.

Table of Contents

Chapters

Wave phenomena and hyperbolic equations

The existence of a solution for a hyperbolic equation and its properties

The construction of asymptotic solutions

Local energy of the wave equation


Additional Material

Reviews

Interesting and welcome little book … provides an excellent introduction to the mathematics of linear wave propagation … This book provides a good introduction to the fascinating topic of linear wave propagation for a reader who has a sound mathematical background but no special familiarity with either the physical or mathematical aspects of wave propagation phenomena.
Mathematical Reviews 
This small book is very carefully written, wellorganized, and hence, highly recommended for graduate students and researchers.
Zentralblatt MATH


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The familiar wave equation is the most fundamental hyperbolic partial differential equation. Other hyperbolic equations, both linear and nonlinear, exhibit many wavelike 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.
Advanced undergraduate and graduate students and researchers interested in partial differential equations and mathematical physics.

Chapters

Wave phenomena and hyperbolic equations

The existence of a solution for a hyperbolic equation and its properties

The construction of asymptotic solutions

Local energy of the wave equation

Interesting and welcome little book … provides an excellent introduction to the mathematics of linear wave propagation … This book provides a good introduction to the fascinating topic of linear wave propagation for a reader who has a sound mathematical background but no special familiarity with either the physical or mathematical aspects of wave propagation phenomena.
Mathematical Reviews 
This small book is very carefully written, wellorganized, and hence, highly recommended for graduate students and researchers.
Zentralblatt MATH