9417238 Bebernes Work supported by this Small Grant for Exploratory Research award seeks to explore the nature of solutions of partial differential equations in the neighborhood of singularities. More precisely, in the evolution of combustion processes, solutions to mathematical models only partially account for a description of the temperature region after reaction begins. Such evolutionary processes are typically initiated by boundary heat addition, by localized volumetric heating, by passage of a dynamic wave or by very fast compression. Localized heating during the ignition period creates regions in which the heat production rate accelerates as the reactants are consumed. These sharply focused hot spots can create explosive bursts of power generation which can trigger the propagation of reaction waves through the medium. It is of both practical importance and theoretical interest to understand how and why detonations might be produced in various circumstances. The goal of this exploratory, high risk project is to attempt to analyze how precisely describable hot spot profiles, known for realistic ignition models, initiate these reaction waves and determine their evolution. ***
