Mathematics

For strictly hyperbolic systems of conservation laws in one space dimension, the Cauchy problem is well posed, within a class of functions having small total variation. However, when solutions with shocks are computed by means of a finite difference scheme, the total variation can become arbitrarily large. As a consequence, convergence of numerical schemes cannot be proved by establishing a priori BV bounds or uniform $\L^1$ stability estimates. In the seminar we discuss this instability by presenting some results in this direction.