Serdica Mathematical Journal, Vol. 26, No 2, (2000), 127p-144p
We treat the oscillatory problem for semilinear wave equation.
The oscillatory initial data are of the type
u(0, x) = h(x) + ε^(σ+1) * e^(il(x)/ε) * b0 (ε, x)
∂t u(0, x) = ε^σ * e^(il(x)/ε) * b1(ε, x).
By using suitable variants of Strichartz estimate we extend the results from
 on a priori estimates of the approximations of geometric optics.The main
improvement is the fact that we can obtain a priori estimates for the case
σ = 1, while in  we could treat only the case σ > n/2 − 1.
The author is partially supported by: M. U. R. S. T. Prog. Nazionale “Problemi e Metodi
nella Teoria delle Equazioni Iperboliche”.