Blow-up phenomenon for a periodic rod equation

In this Letter we consider a new rod equation derived recently by Dai [H.-H. Dai, Acta Mech. 127 (1998) 193] for a compressible hyperelastic material. We explore various sufficient conditions of the initial data which guarantee the blow-up in finite time for periodic case. The focus of this Letter is on two particular classes of initial data, ∫Su0=0 or u0 is odd.