Long-time existence of classical solutions to the Klein-Gordon-Dirac equation in three space dimensions

This thesis studies the almost global existence of classical solutions to the nonlinear hyperbolic system. More precisely, with the system of the Klein-Gordon and wave equations coupled by the nonlinear terms of at least second degree are dealt with. Conditions are given that guarantee the almost global existence of the solutions of the system. It is also shown that the rate of decay of these solutions, for almost global time, is the same,as the rate of the decay of the linear Klein-Gordon and the linear wave equations. The result is applied to prove almost global existence of the Klein-Gordon-Dirac equations of the relativistic quantum mechanics