Variations on the wave equation

A lot of vibration processes in mathematical physics are described by the w ave equation or by related equations and systems, and plenty of research ha s been done on this subject. The results and methods obtained thereby have been very important in other fields of application, and they still are. The y also had and still have an immense influence on the development of mathem atics as a whole. The following survey tries to convey an impression of how exciting the rese arch in this field of partial differential equations has been in the 20th c entury, and it wants to present some of the interesting results achieved. T he selection, of course, reflects personal tastes and interests. It starts reporting on the state of the art at the end of the last century. It then d escribes important solution methods typical for this century, as there are integral equation methods, Hilbert space methods, or spectral representatio n. Generalized solutions to initial-boundary-value problems are mentioned, and some applications are indicated, e.g. on the asymptotic behaviour of so lutions, in scattering theory, and in non-linear analysis. Copyright (C) 20 01 John Wiley & Sons, Ltd.