Analysis of explosion for nonlinear Volterra equations

This survey paper presents some analytical tools for determining the existence of a blow-up solution for a wide class of nonlinear Volterra integral equations. The related phenomenon of quenching has also been investigated using similar techniques. In both cases, lower and upper bound estimates for the critical time, as well as asymptotic solution behavior in the key limit are established. This paper surveys recent results in the analysis of such problems and proposes problems for future study.