Propagation des oscillations dans deux classes de systemes hyperboliques (2∗2et3∗3)
- 1 January 1988
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 13 (8) , 905-925
- https://doi.org/10.1080/03605308808820564
Abstract
We study in this note the solutions of two types of hyperbolic systems of conservation laws with oscillating data. The first one (a2∗2 system) has only one linearly degenerate eigenvalue. Using the results of R.J.Di Perna related to genuinely nonlinear fields, one can describe the propagatrion of oscillations (which appear in only one direction) with an integro differential system for which one of the two unknowns is a field depending, of y ∊ ]0,1[, in addition of x and t. The second system is a linearly degenerate 3∗3 system. We apply theory of compensated compactness, due to L. Tartar and F. Murat and, in the same way as above, we show that the initial oscillations can propagate; this propagation is then described witha a relaxed system of 3 unknownsKeywords
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