Blowup for systems of conservation laws

We give examples of finite time blowup in sup-norm and total variation for 3 x 3-systems of strictly hyperbolic conservation laws. The exact solutions are explicitly constructed. In the case of sup-norm blowup we also provide an example where all other p-norms, 1 less than or equal to p < infinity, remain uniformly bounded. Finally we consider appropriate rescalings for the different types of blowup.