Hyperbolic partial differential equations and wave phenomena
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Bibliographic Information
Hyperbolic partial differential equations and wave phenomena
（Translations of mathematical monographs, v. 189）（Iwanami series in modern mathematics）
American Mathematical Society, c2000
- Other Title
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偏微分方程式2
Partial differential equations 2
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Other title from t.p. verso
Originally published: Tokyo : Iwanami Shoten, 1997
Bibliography: p. 179-180
Includes index
Description and Table of Contents
Description
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.
Table of Contents
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 Perspectives on current research in mathematics Bibliography Solutions to the exercises Index Copy/reprinting (cont'd).
by "Nielsen BookData"