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

Some simple examples of nonstrictly hyperbolic conservation laws are p resented 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 wit h erroneous qualitative behaviour; another example shows that the appr oximate solution is not well defined. For both of these examples, a cl assical, 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.