THE SOLUTION OF NONSTRICTLY HYPERBOLIC CONSERVATION-LAWS MAY BE HARD TO COMPUTE

Some simple examples of nonstrictly hyperbolic conservation laws are presented that admit certain instability properties with respect to L(1)-perturbations of the initial data. One of the examples shows that a piecewise constant approximation generates an approximate solution with erroneous qualitative behaviour; another example shows that the approximate solution is not well defined. For both of these examples, a classical, stable entropy solution can be given by an explicit formula. These properties may cause difficulties for numerical methods based on die solution of Riemann problems.