Blow-up of periodic solutions to linearly degenerate quasilinear hyperbolic systems

An example is given to show that for the Cauchy problem of n×n$n\times n$ homogeneous linearly degenerate quasilinear hyperbolic systems with periodic initial data, when n>2$n>2$, C¹$C^1$ solutions may blow up in a finite time, no matter how small and smooth the initial data are.