Hyperbolic Partial Differential Equations and Wave Phenomena

Hyperbolic Partial Differential Equations and Wave Phenomena
Author: Mitsuru Ikawa
Publisher: American Mathematical Soc.
Total Pages: 218
Release: 2000
Genre: Mathematics
ISBN: 9780821810217


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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 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.


Hyperbolic Partial Differential Equations and Wave Phenomena
Language: en
Pages: 218
Authors: Mitsuru Ikawa
Categories: Mathematics
Type: BOOK - Published: 2000 - Publisher: American Mathematical Soc.

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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
Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena
Language: en
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Authors: Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
Categories: Mathematics
Type: BOOK - Published: 2010-10-01 - Publisher: American Mathematical Soc.

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This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Non
Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena
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Pages: 389
Authors: Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
Categories: Differential equations, Hyperbolic
Type: BOOK - Published: 2010 - Publisher:

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Type: BOOK - Published: 2014-07-24 - Publisher: Walter de Gruyter GmbH & Co KG

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The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an internati
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Language: en
Pages: 330
Authors: Willy Dörfler
Categories: Mathematics
Type: BOOK - Published: 2020-10-01 - Publisher: Springer Nature

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Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and