  We discuss the Cauchy problem for anisotropic wave equations. Precisely, we
address the question to know which kind of Cauchy data on the lateral boundary
are necessary to guarantee the uniqueness of continuation of solutions of an
anisotropic wave equation. In the case where the uniqueness holds, the natural
problem that arise naturally in this context is to estimate the solutions, in
some appropriate space, in terms of norms of the Cauchy data. We aim in this
paper to convert, via a reduced Fourrier-Bros-Iagolnitzer transform, the known
stability results on the Cauchy problem for elliptic equations to stability
results on the Cauchy problem for waves equations. By proceeding in that way
the main difficulty is to control the residual terms, induced by the reduced
Fourrier-Bros-Iagolnitzer transform, by the Cauchy data. Also, the uniqueness
of continuation from Cauchy data is obtained as byproduct of stability results.
