Periodic Structure in Two-dimensional Riemann Problems for Hamilton-jacobi Equations Periodic Structure in Two-dimensional Riemann Problems for Hamilton-jacobi Equations

of the Dissertation Periodic Structure in Two-Dimensional Riemann Problems for Hamilton-Jacobi Equations by John Dominick Pinezich Doctor of Philosophy in Applied Mathematics and Statistics State University of New York at Stony Brook 1998 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 twodimensional Riemann solutions, this dissertation shows that examples of Riemann problems with Riemann solutions of comparable complexity do in fact exist. iii To my wife Ginger, and my daughter Meghan Table of