Mathematical Sciences: The Mathematics of Thermal Explosion Phenomena

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This research is focused on a mathematical analysis of models arising from the study of reactive thermal explosions. Initial value problems that describe the evolution of diffusive and nondiffusive thermal explosions in confined domains will be analyzed. Also of interest is the prediction of exactly when thermal explosions will occur, the location in the confined vessel where hotspots will develop, and a description of precisely how the blowup singularities evolve as the blowup time is approached. The mathematical models which describe these problems are partial differential equations with mixed parabolic-hyperbolic behavior. These models include the interaction between chemical processes and the the induced gasdynamic phenomena. An understanding of this interaction is needed if progress is to be made on ignition explosions, high speed deflagrations, detonations, and the transition of flames to detonations. These topics are vital in the study of accidental explosions.