GLOBAL SOLUTIONS OF THE EXPONENTIAL WAVE EQUATION WITH SMALL INITIAL DATA

We study the initial value problem of the exponential wave equation in Rn+1 for small initial data. We shows, in the case of n = 1, the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When n >= 2, a vector field method is applied to show the stability of a trivial solution phi = 0.