Wave Equation

Abstract

The ideas in this chapter are built around a study of the one-dimensional wave equation

$$ {u_{tt}} - {c^2}{u_{xx}} = 0, $$

((V))

also called the vibrating string equation. This equation and its higher-dimensional version

$$ {u_{tt}} - {c^2}\Delta u = 0 $$

((W))

also governs many other phenomena, e.g., sound waves, electromagnetic waves, and is of great interest in its own right. It is also, however, representative of the large class of hyperbolic partial differential equations, and it is useful to meet fundamental properties of this class in this relatively simple case.