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

Ikawa, Mitsuru

 
9780821810217: Hyperbolic Partial Differential Equations and Wave Phenomena (Translations of Mathematical Monographs)
Softcover
ISBN 10: 0821810219 ISBN 13: 9780821810217
Verlag: American Mathematical Society, 2000

Inhaltsangabe

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.

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Críticas

... provides an excellent introduction to the mathematics of linear wave propagation (Mathematical Reviews )

Reseña del editor

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.

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Verlag
American Mathematical Society
Erscheinungsdatum
2000
Sprache
Englisch
ISBN 10 
0821810219
ISBN 13 
9780821810217
Einband
Tapa blanda
Anzahl der Seiten
190
Kontakt zum Hersteller
Nicht verfügbar
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