On coupled Klein-Gordon-Schrödinger equations, II

A classical model that describes a system of conserved scalar nucleons interacting with neutral scalar mesons is considered. The dynamics of these fields are coupled through the Yukawa interaction. In the case of relativistic fields, that is, when nucleons are described by Dirac spinor fields, the coupled Klein-Gordon-Dirac equations are encountered. Both Klein-Gordon-Dirac equations and Klein-Gordon-Schroedinger equations have energy forms indefinite in nature. The initial-boundary value problem for the coupled Klein-Gordon-Schroedinger equations in three space dimensions is discussed here. The purpose is to establish the existence and uniqueness theorems of global C/sup x/-solutions of the initial-boundary value problem. The main difficulties lie in the proof of the existence of strong solutions and their regularity properties. (RWR)