Acoustic and Electromagnetic Equations

Acoustic and electromagnetic waves underlie a vast range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. Mathematical modelling of these waves has undergone a considerable growth in recent years, and this timely book written by a leading international researcher presents some of the research in a careful and complete way. Graduate students in mathematics, physics, and engineering will find this book of interest.

From the reviews:

MATHEMATICAL REVIEWS

"A remarkable feature of this book is that this rather classical topic of applied mathematics is not approached in the framework of classical Holder spaces but is linked up with concepts of Sobolev spaces and variational methods. This feature gives this monograph a modern feel. On the other hand it has also a quite down to earth flavor, since it includes conrete calculations such as elaborate discussion of the case of the sphere as the domain boundary. That the book is based on lecture notes is still noticeable and makes it comfortable to read and suitable for self-study."

"The book investigates special solutions to two classical hyperbolic equations the wave equations and the Maxwell equations on Minkowski space. The choice of material is guided by the needs of applications in mathematical physics and engineering, and the book is suitable for graduate students." (European Mathematical Society Newsletter, September, 2002)

"A remarkable feature of this book is that this rather classical topic of applied mathematics is linked up with concepts of Sobolev spaces and variational methods. This feature gives this monograph a modern feel. On the other hand it has also a quite down to earth flavour, since it includes concrete calculations . That the book is based on lecture notes is still noticeable and makes it comfortable to read and suitable for self-study." (Rainer Picard, Mathematical Reviews, Issue 2002 c)

"This book is based on lectures held by the author and is intended for graduate students in mathematics, physics, and engineering. It is self-contained and should be useful to anyone interested in problems of acoustic and electromagnetics." (Johannes Elschner, Zentralblatt MATH, Vol. 981, 2002)

"The book is a detailed description of the theory of classical boundary value problems . A very deep and detailed analysis for the case of a spherical obstacle ispresented. This book stands out for an extremely careful and thorough discussion of necessary functional spaces and other auxiliary facts which makes it completely self-contained. Careful and complete proofs are given throughout. This is an indispensable reading for any person interested in boundary value problems for the time-harmonic wave equations." (V. V. Kravchenko, Zeitschrift für Analysis und ihre Anwendungen, Vol. 21 (1), 2002)

Contenu
1 Some Wave Equations.- 2 The Helmholtz Equation.- 3 Integral Representations and Integral Equations.- 4 Singular Integral Operators.- 5 Maxwell Equations and Electromagnetic Waves.- References.