Existing combustion books are primarily phenomenological in the sense that explanation, where provided, is usually set in an intuitive framework; when mathematical modeling is employed it is often obscured by ad hoc irrational approximation, the emphasis being on the explanation of existing experimental results. It is hardly necessary to add that the philosophy underlying such texts is scientifically legitimate and that they will undoubtedly stay in the mainstream of combustion science for many years to come. Nevertheless, we are of the opinion that there is need for texts that treat combustion as a mathematical science and the present work is an attempt to meet that need in part.

In this monograph we describe, within a mathematical framework, certain basic areas of combustion science, including many topics rightly covered by introductory graduate courses in the subject. Our treatment eschews sterile rigor inappropriate for a subject in which the emphasis has been physical, but we are deeply concerned with maintaining clear links between the mathematical modeling and the analytical results; irrational approximation is carefully avoided. All but the most fastidious of readers will be satisfied that the mathematical conclusions are correct, except for slips of the pen.

Although the material covered inevitably reflects our special interests and personal perspectives, the entire discussion is connected by a singular perturbation procedure known as activation-energy asumptotics. The description of reacting systems characterized by Arrhenius kinetics can be simplified when the activation energy is large, corresponding to an extreme sensitivity to temperature.