Global solutions with a single transonic shock wave for quasilinear hyperbolic systems (Q1368563)

The author studies global solutions containing a single transonic shock wave for the general quasilinear hyperbolic system \(U+F=G\) which is considered in one-dimensional space. The presence of \(G\) brings about secondary waves. The author singles out the amount of such waves along each characteristic field and shows that global-in-time solutions exist provided the total variation of \(U\), \(|G|\), and the total amount of secondary waves along the transonic characteristic are sufficiently small.