Blow-up criteria for modified two-component generalization of hyper-elastic rod equation

Abstract

We investigate the blow-up phenomena for the two-component generalization of hyper-elastic rod equation on the real line. We establish some blow-up criteria for system of coupled equations with density function that in one case alternates its sign and keeps its sign in another case under certain natural initial profiles. Presented results extend and specify the earlier blow-up criteria for such type system.