Growth rates for blow-up solutions of nonlinear Volterra equations. (English) Zbl 0916.45007
Summary: An investigation is made of the blow-up growth property of the solution to certain nonlinear Volterra integral equations which model explosive behavior in a diffusive medium. The basic results provide the asymptotic form of the blow-up solution for a large class of kernels as well as various nonlinearities based on examples from solid combustion and adiabatic shear band formation.
MSC:
45G05 | Singular nonlinear integral equations |
45M05 | Asymptotics of solutions to integral equations |
80A25 | Combustion |