NONLINEAR HYPERBOLIC OSCILLATIONS METHODS AND QUALITATIVE RESULTS

One studies the Cauchy problem for hyperbolic systems of first order conservation laws partial (t)u + partial (x)f (u) = 0, with an oscillating sequence of initial data. The oscillations have an O(1)amplitude; one may think to u-epsilon(x,0) = [GRAPHICS] where a(x, .) is periodic. It turns out that one part of the initial oscillations are killed because of genuine non-linearity. But the most of the physically relevant systems are endowed with at least one linearly degenerate characteristic field, which allows oscillations of a part of the field u.