Figure 1: Graphical representation of the flux function and of fa, pa and p* Figure 2: A particular configuration of discontinuities with the SV trajectory. Figure 3: Two waves interact together producing a third wave Figure 5: Interaction coming from the right with the SV trajectory cancelling (Case a)) or creating (Case b)) a non classical shock. Figure 7: px € (0, fal, pr € [0, Pal U [fa, p*| and pr + pr < p*. Interaction coming from the left with the SV trajectory. Figure 6: Interaction coming from the left with the SV trajectory cancelling (Case a)) or creating (Case b)) a non classical shock. Figure 10: An example of a NC3) interaction (Case a)) and of a NC4) interaction (Case b)) Figure 11: Interactions with the SV trajectory (---). e the NC3 interactions (the evolution of tangent vectors is described in (28), Figure 10 a)) We can notice that if a wave k interacts with the SV trajectory n times then W,’ will be decomposed into a sum of n terms. We want to find a bound of W;? which does not depend on n. For instance, we have The two following points are the main tools to prove Lemma 13: By straightforward computations, we conclude that References
