On the breakdown of solutions to N×N quasilinear hyperbolic systems Original Research Article

We shall be concerned with the development of singularities of the C1-solutions of the quasilinear N×N hyperbolic system Ut+A(U)Ux=0 in one space dimension. Generalizing a nonlinearity condition introduced by MacCamy and Mizel (Arch. Rat. Mech. Anal. 25 (1967) 299–320), in this paper we prove some results of blow-up for the first-order derivatives without restrictions on the size of the initial data.