Blow-up solutions to a system of nonlinear Volterra equations

A system of nonlinear Volterra integral equations with convolution kernels is considered. Estimates are given for the blow-up time when conditions are such that the solution is known to become unbounded in finite time. For two examples that arise in combustion problems, numerical estimates of blow-up time are presented. Additionally, the asymptotic behavior of the blow-up solution in the key limit is established for the power-law and exponential nonlinearity cases.