| This dissertation investigates the structure of two-dimensional Riemann problems for Hamilton-Jacobi equations. We show that it is possible for the Riemann solution to have closed characteristic orbits, enclosing furthermore a periodic sonic structure, which in turn encloses a parabolic structure. This investigation was prompted by a numerical construction of a Riemann solution for a particular example displaying an even richer internal structure. Since there are no (known) robust methods to numerically construct two-dimensional Riemann solutions, this dissertation shows that examples of Riemann problems with Riemann solutions of comparable complexity do in fact exist. |
