Variations on the wave equation (Q5890235)

This paper is a survey on methods for investigation of wave equations, developed during 20th century. The vibration processes in mechanics and other areas of physics are described by the wave equation or by related equations and systems. The results and methods obtained thereby have been very important in other fields of application, and they still are. They also had and still have an immense influence on the development of mathematics as a whole. The author considers some important methods, for instance, integral equation methods, Hilbert space method and spectral representation. Generalized solutions to initial-boundary value problems are mentioned, and some applications are indicated. The reader is referred to a list of 115 books and papers where one may find a description of the methods for solving wave equations.