| Abstract: |
| We consider a class of Gowdy spacetimes that reduces the Einstein`s field equation to a system of two semilinear wave equations, by assuming a universe without matter, in which the gravitational wave fronts repeat in space and are mutually parallel. To prove the existence of local solutions of the system, in the literature only certain formal expansions near the Big Bang singularity are investigated. Nevertheless we aim at a rigorous proof. The main idea is to apply the Lyapunov-Schmidt reduction, for which we establish a functional setting that fits to the nonlinearity, and then solve the related small-divisor problem. |
|