Breakdown of classical solutions to the Cauchy problem on a semi-bounded initial axis for quasilinear hyperbolic systems

In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Under the assumptions that the rightmost (resp. leftmost) eigenvalue is not weakly linearly degenerate and the source term satisfies the corresponding matching condition, we obtain a blow-up result of a C1 solution with small and decaying initial data.