Abstract :
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 R2 is
presented. This method is based on a detailed investigation of the respective
overdetermined system and on a special construction, involving Pfaff systems
