Formation of Singularities for Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity

Abstract

In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Without restriction on characteristics with constant multiplicity (> 1), a blow-up result is obtained for the C¹ solution to the Cauchy problem under the assumptions where there is a simple genuinely nonlinear characteristic and the initial data possess certain weaker decaying properties.