A new upper estimation for the blow-up time of solutions of a Volterra integral equation and its application to the modeling of the formation of shear bands

The estimation of the blow-up time of a class of Volterra integral equations of convolution type is studied. A new upper estimate of the blow-up time, expressed in terms of the convergence of a certain integral, is found. Moreover, it turns out that the aforementioned upper estimate can be applied to an even more general class of Volterra integral equations, like the one describing the formation of shear bands in steel.