Asakura, Fumioki Global solutions with a single transonic shock wave for quasilinear hyperbolic systems. (English) Zbl 0886.35092 Methods Appl. Anal. 4, No. 1, 33-52 (1997). 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. Reviewer: K.Kajitani (Ibaraki) Cited in 4 Documents MSC: 35L60 First-order nonlinear hyperbolic equations 35L67 Shocks and singularities for hyperbolic equations Keywords:secondary waves; transonic characteristic PDFBibTeX XMLCite \textit{F. Asakura}, Methods Appl. Anal. 4, No. 1, 33--52 (1997; Zbl 0886.35092) Full Text: DOI