9R47. Systems of Conservation Laws: Two-Dimensional Riemann Problems. Progress in Nonlinear Differential Equations and Their Applications, Vol 38. - Yuxi Zheng (Dept of Math, Indiana Univ, Bloomington IN 47405). Birkhauser Boston, Cambridge MA. 2001. 317 pp. ISBN 0-8176-4080-0. $69.95.
Reviewed by TH Moulden (Dept of Aerospace Eng, Univ of Tennessee Space Inst, BH Goethert Pkwy, Tullahoma TN 37388-8897).
The text under review is based upon the contents of a course on partial differential equations offered at Indiana University. The subtitle, Two-Dimensional Riemann Problems, indicates the main thrust of the book. However, the early chapters (1–4) are restricted to discussing the basic phenomena in the one-dimensional case. These phenomena include the notion of characteristics and Riemann invariants and, of course, shock waves. Numerical methods are introduced, but not in detail. Glimm’s scheme is also introduced at this point. Difficulties in finding solutions (as stated in the von Neumann paradoxes)...
