Hyperbolic Partial Differential Equations and Wave Phenomena (Translations of Mathematical Monographs) - Softcover

Mitsuru Ikawa

Softcover

ISBN 10: 0821810219 ISBN 13: 9780821810217

Publisher: American Mathematical Society, 2000

Synopsis

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.

About this title

From the Publisher

Hyperbolic Partial Differential Equations and Wave Phenomena - Ikawa

This small book is very carefully written, well-organized, and hence, highly recommended for graduate students and researchers.

Zentralblatt f\"ur Mathematik

Review

This small book is very carefully written, well-organized, and hence, highly recommended for graduate students and researchers. --Zentralblatt für Mathematik

Edition details

• Publisher: American Mathematical Society
• Publication date: 2000
• ISBN 10: 0821810219
• ISBN 13: 9780821810217
• Binding: Paperback
• Language: English
• Number of pages: 190