This is a three-year cooperative proposal between Dr. Haitao Fan of Georgetown University and Dr. Tong Yang of the City University of Hong Kong. Dr. Fan requests two visits, one in the summer of 2001 and the other in the summer of 2003 for conducting a joint research on hyperbolic partial differential equations (PDE) for reactive flow equations. Both the U.S. and Hong Kong P.I.s are experienced researchers in this field. The application of the PDE to reactive flow equations is a promising research area and can continue keep the U.S. at the forefront of an important mathematical field.