The asymptotic behavior for gaseous ignition models

The blowup asymptotics for classical solutions of ut = Δu + eu + g(t) are analyzed, including the nonlocal case where g has a functional dependence of the form ∫ωutdx. The method of analyzing the evolution of the blowup singularity is a dynamical systems approach using center manifold techniques and analyzing an ω-limit set for a corresponding Hamilton-Jacobi equation.