Messaoudi, S. A. Development of singularities in solutions of a hyperbolic system. (English) Zbl 1023.35064 Int. J. Math. Math. Sci. 28, No. 1, 1-7 (2001). The system considered has the form \[ u_t=f\left({v \over 1+au} \right)v_x,\;v_t=u_x,\;a=\text{const.},\;f\geq 0. \] It is shown that \(C^1\)-solutions blow up even for small initial data. Reviewer: G.Boillat (Aubière) Cited in 16 Documents MSC: 35L45 Initial value problems for first-order hyperbolic systems 35L67 Shocks and singularities for hyperbolic equations 35L60 First-order nonlinear hyperbolic equations Keywords:blow up for small initial data PDFBibTeX XMLCite \textit{S. A. Messaoudi}, Int. J. Math. Math. Sci. 28, No. 1, 1--7 (2001; Zbl 1023.35064) Full Text: DOI EuDML