## Un système hyperbolique non linéaire avec des données oscillantes. (Oscillating data in one nonlinear hyperbolic system).(French)Zbl 0606.35050

One consider high-frequency oscillations, with ordinary amplitude, in the hyperbolic, nonlinear system: $$w_ t+zw_ x=F(w,z)$$, $$z_ 1+wz_ x=G(w,z)$$. A new variable $$y\in]0,1[$$ is introduced. The propagation is governed by an integro-differential system of a new type, in two unknowns functions W(x,t,y), Z(x,t,y).

### MSC:

 35L60 First-order nonlinear hyperbolic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs