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Development of singularities in solutions of a hyperbolic system. (English) Zbl 1023.35064

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.

MSC:

35L45 Initial value problems for first-order hyperbolic systems
35L67 Shocks and singularities for hyperbolic equations
35L60 First-order nonlinear hyperbolic equations
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