## ABSTRACT

THE WAVE EQUATION

The purpose of this chapter is to study the one dimensional wave equation

utt(x; t) = a 2uxx(x; t) + h(x; t); x 2 (a; b) R; t > 0;

also known as the vibrating string equation, and its higher dimensional version

utt(x; t) = a 2u(x; t) + h(x; t); x 2 Rn; n = 2; 3:

This equation is important in many applications and describes many physical phenomena, e.g., sound waves, ocean waves and mechanical and electromagnetic waves. As mentioned in the previous chapter, the wave equation is an important representative of the very large class of hyperbolic partial dierential equations.