Memoirs of the American Mathematical Society 1999; 77 pp; softcover Volume: 137 ISBN10: 0821809474 ISBN13: 9780821809471 List Price: US$45 Individual Members: US$27 Institutional Members: US$36 Order Code: MEMO/137/654
 In this volume, the onedimensional and twodimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1D or 2D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which havea been merely discussed so far. The generalized RankineHugoniot and entropy conditions for Dirac delta waves are clarified with viscous vanishing method. All of the existence, uniqueness and stability for viscous perturbations are proved analytically. Readership Graduate students and research mathematicians working in nonlinear PDEs; numerical analysts working in fluid dynamics. Table of Contents  Introduction
 1D Riemann problem for transportation equations in gas dynamics
 2D Riemann problem for transportation
 References
