Explosion in a Diffusive Strip due to a Source with Local and Nonlocal Features

The possibility of a blow-up solution to the one-dimensional heat equation is examined for a nonlinear source that combines local and nonlocal features. The problem is analyzed by reduction to a pair of coupled nonlinear Volterra equations, for which existence as well as nonexistence through blow-up is investigated. Blow-up always occurs for the Neumann problem, whereas for the Dirichlet problem, blow-up depends upon the magnitude of certain parameters. An example is worked out that includes an asymptotic analysis to determine the growth rate near blow-up.