| Abstract: | In this paper we consider the initial value problem for the nonlinear wave equation □u = F(u, u′) in Friedman-Robertson-Walker space-time, □ being the D'Alambertian in local coordinates of space-time. We obtain decay estimates and show that the equation has global solutions for small initial data. We do it by reducing the problem to an initial value problem for the wave equation over hyperbolic space. As byproduct we derive decay and global existence for solutions of the wave equation over the hyperbolic space with small initial data. The same technique with some auxiliary lemmas similar to the ones proved in 6], 7] can be used to generalize the result to the case when F depends also on second derivatives of u in a certain way. |
