Singularity formation in systems of non-strictly hyperbolic equations (original) (raw)

We analyze finite time singularity formation for two systems of hyperbolic equations. Our results extend previous proofs of breakdown concerning 2 × 2 non-strictly hyperbolic systems to n × n systems, and to a situation where, additionally, the condition of genuine nonlinearity is violated throughout phase space. The systems we consider include as special cases those examined by Keyfitz and Kranzer and by Serre. They take the form ut + (φ(u)u)x = 0, where φ is a scalar-valued function of the n-dimensional vector u, and ut + Λ(u)ux = 0, under the assumption Λ = diag