Abstract :
In parts I, II, and III combined of this paper, we define a notion of viscosity solution
for these equations and existence is proved by a Perron-like method. Here, in part I, we
prove useful identities, and a maximum-like principle for smooth sub(super) solutions of
the standard wave equation. We define a new potential theoretic (P) notion of solution,
subsolution and supersolution, and a related potential type (P) Cauchy problem for
semilinear second order hyperbolic equations.
2002 Elsevier Science (USA). All rights reserved.
