Simple waves and simple states in R-2

[摘要] The so-called ''solutions, constructed by means of Riemann invariants'' for quasi-linear systems of PDEs, play an important role in gas dynamics, since they describe the propagation and the superposition of waves. The existing methods for finding solutions (simple waves and simple states) of this type usually deal with systems whose coefficients do not depend on the independent variables, and have a very limited application to non-homogeneous systems. In this paper a method for finding such solutions in the case of general quasi-linear systems of PDEs in R-2 is presented. This method is based on a detailed investigation of the respective overdetermined system and on a special construction, involving Pfaff systems. (C) 1997 Academic Press.

[发布日期] 1997-10-15