Mathematical Sciences: RUI: Mathematical Problems from Combustion Theory

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With this award the principal investigators will continue their mathematical analysis of models of reactive thermal explosions. In particular, they will analyze the solutions of initial-boundary value problems that describe the evolution of diffusive and nondiffusive thermal explosions in confined domains, in order to determine where and when explosions will take place. With regard to these latter questions the principal investigators will describe precisely how the blowup singularities evolve in space and time as the blowup time is reached. Natural phenomena involving burning and explosions offer important scientific and technological areas of investigation. As with many physical processes there are generally two avenues for study: the theoretical and the experimental. This award represents the theoretical approach to combustion. In it the principal investigators will use mathematical analysis to determine where and when explosions occur in models of thermally reactive systems in containers and the locations of hotspots.