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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
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