Acoustic and Electromagnetic Equations

Integral Representations for Harmonic Problems
1. Auflage. Softcover version of original hardcover Auflage 2001
ISBN: 978-1-4419-2889-4
Verlag: Springer

Buch, Englisch, Band 144, 318 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 1030 g

Reihe: Applied Mathematical Sciences

This book is devoted to the study of the acoustic wave equation and of the Maxwell system, the two most common wave equations encountered in physics or in engineering. The main goal is to present a detailed analysis of their mathematical and physical properties. Wave equations are time dependent. However, use of the Fourier trans­ form reduces their study to that of harmonic systems: the harmonic Helmholtz equation, in the case of the acoustic equation, or the har­ monic Maxwell system. This book concentrates on the study of these harmonic problems, which are a first step toward the study of more general time-dependent problems. In each case, we give a mathematical setting that allows us to prove existence and uniqueness theorems. We have systematically chosen the use of variational formulations related to considerations of physical energy. We study the integral representations of the solutions. These representa­ tions yield several integral equations. We analyze their essential properties. We introduce variational formulations for these integral equations, which are the basis of most numerical approximations. Different parts of this book were taught for at least ten years by the author at the post-graduate level at Ecole Poly technique and the University of Paris 6, to students in applied mathematics. The actual presentation has been tested on them. I wish to thank them for their active and constructive participation, which has been extremely useful, and I apologize for forcing them to learn some geometry of surfaces.

Zielgruppe

Research

Autoren/Hrsg.

Nedelec, Jean-Claude

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Naturwissenschaften Physik Elektromagnetismus Elektrizität, Elektrodynamik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Naturwissenschaften Physik Mechanik Akustik, Schwingungsanalyse

Inhaltsverzeichnis

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.