Mathematical Sciences: Mathematical Problems from CombustionTheory

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In this project the principal investigators will analyze systems of differential equations whose solutions model several types of reactive thermal explosions. In particular, they will study the qualitative properties of solutions of initial-boundary value problems that describe the evolution of diffusive and nondiffusive thermal explosions in finite domains. The goal of this investigation is to predict precisely where and when explosions will occur and to study how the solution behaves as the blow-up time approaches. Combustion phenomena are common in many aspects of our daily lives; think of cars, kitchens, heating systems, rocket and missile engines. A large amount of computer power is brought to bear upon the systems of partial differential equations that describe combustion and explosion phenomena, but very often a great deal of insight can be obtained from a mathematical analysis of the governing equations. For example, in this project the principal investigators will attempt to predict where and when an explosion will occur in a confined space by means of a judicious use of a'priori estimates and bounding functions.