Free boundary problems arising in shock reflection have been solved for regular shock reflection in a model equation; the method will be extended to a larger set of equations and other types of shock reflection. Solving a prototype problem for the gas dynamics equations is in sight. Other two-dimensional Riemann problems, such as reflection of rarefaction waves at the sonic line, will be considered. A different free boundary problem, with connections to new kinds of singularities, occurs in this case. By constrast with shock reflection problems, in which the complicated behavior occurred in the subsonic region and was analysed using Holder estimates for degenerate elliptic equations, the interaction of rarefaction waves with the sonic boundary involves study of degenerate hyperbolic eigenvalue problems.
The PI has had success, particularly with women graduate students and postdoctoral visitors, in introducing beginning researchers to her areas in conservation laws, and in helping to expand their career horizons. It is planned to mentor two postdocs (at least one, already selected, is a woman), including encouraging their teaching and professional development in ways such as writing proposals, refereeing papers, and participating in conferences. In addition, the second research topic is strongly interdisciplinary, and the PI's work has aroused some positive interest in the multifluid science community. The PI and co-workers will attend and make presentations at engineering conferences, write articles for journals on multiphase flow to explain the results, and organize sessions at conferences to bring together mathematical, computational and experimental researchers in multifluid science.
