Global solutions to wave equations — existence theorems

Abstract

We shall start with the formulation of a global existence theorem for solutions of a class of nonlinear wave equations. The first theorem, Theorem 1.1, is typical for the kind of existence theorems that will be obtained for other evolution equations in Chapter 11. The second theorem, Theorem 1.2, optimizes in some sense the result for wave equations. We shall conclude this section with giving a few examples characterizing the behaviour of solutions to nonlinear wave equations in general, thus pointing out the crucial parts of the assumptions in the existence theorems.