Weak limits of semilinear hyperbolic systems with oscillating data. (English) Zbl 0588.76137

McLaughlin, D.; Papanicolaou, G.; Tartar, L.

Macroscopic modelling of turbulent flows, Proc. Workshop, Sophia- Antipolis/France 1984, Lect. Notes Phys. 230, 277-289 (1985).

[For the entire collection see Zbl 0561.00024.]
We consider several examples of nonlinear evolution equations with initial data that are rapidly oscillating functions of the space variable. We obtain an effective system of nonlinear evolution equations for the various moments of the solution by a multiple scale method. We also show how in one case (the Carleman model) compensated compactness gives a very general way of obtaining the effective equations without the use of multiple scales.

MSC:

76P05	Rarefied gas flows, Boltzmann equation in fluid mechanics
35L60	First-order nonlinear hyperbolic equations

Keywords:

Broadwell equations; simple model for Boltzmann equation; nonlinear evolution equations; rapidly oscillating functions; moments of the solution; multiple scale method; Carleman model

Citations:

Zbl 0561.00024