This report is Chapter VII of the twelve in a forthcoming research monograph on the mathematical theory of laminar combustion. Cylindrical and spherical premixed flames are discussed, the latter with a view to application to the burning monopropellant drop. Cylindrical flames have a planar character, while spherical flames exhibit ignition and extinction.

This report is Chapter VI of the twelve in a forthcoming research monograph on the mathematical theory of laminar combustion. Spherical diffusion flames are discussed with a view to application to the burning fuel drop. Emphasis is on establishing ignition and extinction conditions. (Author).

An earlier paper (MRC TSR no. 1803) indicated that rational analysis of the governing equations of combustion can be based on activation-energy asymptotics. As an example, the basic problem of combustion theory is treated, namely the premixed plane flame (i.e. the unlimited one-dimensional steady solution).

This monograph deals with the structure, generation and stability of flames from a mathematical point of view. It uses a specific mathematical approach to provide a unified theoretical description of fundamental flame phenomena. Its importance stems from the fact that it provides the first clear evidence that combustion can be legitimately treated as a mathematical science as well as an empirical one. The book will be of interest to researchers in combustion, fluid mechanics and applied mathematics, as well as to graduate students taking advanced courses in these areas.