The Riemann problem for the transportation equations in gas dynamics
About this Title
Wancheng Sheng and Tong Zhang
Publication: Memoirs of the American Mathematical Society
Publication Year 1999: Volume 137, Number 654
ISBNs: 978-0-8218-0947-1 (print); 978-1-4704-0243-3 (online)
MathSciNet review: 1466909
MSC (1991): Primary 35Q35; Secondary 35L65, 76N10, 76N15
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.
Table of Contents
- I. Introduction
- II. 1-D Riemann problem for the transportation equations in gas dynamics
- III. 2-D Riemann problem for the transportation equations in gas dynamics