On the existence of the solution of Burger's equation for .
We propose a necessary and sufficient condition about the existence of variations, i.e., of non trivial solutions to the differential inclusion .
In this paper we prove the existence of a weak solution for a given semilinear singular real hyperbolic system.
Following the ideas of D. Serre and J. Shearer (1993), we prove in this paper the existence of a weak solution of the Cauchy problem for a given second order quasilinear hyperbolic equation.
A simpler proof of a result of Burq [1] is presented.