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The Riemann Problem for the Transportation Equations in Gas Dynamics
Tong Zhang, Academia Sinica, Beijing, People's Republic of China, and Wancheng Sheng, Xinjiang University, Urumuqi, People's Republic of China
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Memoirs of the American Mathematical Society
1999; 77 pp; softcover
Volume: 137
ISBN-10: 0-8218-0947-4
ISBN-13: 978-0-8218-0947-1
List Price: US$48 Individual Members: US$28.80
Institutional Members: US\$38.40
Order Code: MEMO/137/654

In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D 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 Rankine-Hugoniot 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.

Graduate students and research mathematicians working in nonlinear PDEs; numerical analysts working in fluid dynamics.

• Introduction
• 1-D Riemann problem for transportation equations in gas dynamics
• 2-D Riemann problem for transportation
• References