This IMA Volume in Mathematics and its Applications DYNAMICAL ISSUES IN COMBUSTION THEORY is based on the proceedings of a workshop which was an integral part of the 1989-90 IMA program on "Dynamical Systems and their Applications." The aim of this workshop was to cross-fertilize research groups working in topics of current interest in combustion dynamics and mathematical methods applicable thereto. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee, George R. Sell, Paul Fife, Amable Liiian and Foreman Williams for organizing the meeting. We especially thank Paul Fife, Amable Liiilin and Foreman Williams for editing the proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, the National Science Foundation and the Office of Naval Research. Avner Friedman Willard Miller, Jr. ix PREFACE The world ofcombustion phenomena is rich in problems intriguing to the math ematical scientist. They offer challenges on several fronts: (1) modeling, which involves the elucidation of the essential features of a given phenomenon through physical insight and knowledge of experimental results, (2) devising appropriate asymptotic and computational methods, and (3) developing sound mathematical theories. Papers in the present volume, which are based on talks given at the Workshop on Dynamical Issues in Combustion Theory in November, 1989, describe how all of these challenges have been met for particular examples within a number of common combustion scenarios: reactiveshocks, low Mach number premixed reactive flow, nonpremixed phenomena, and solid propellants.

Klappentext

The world of combustion phenomena is rich in problems intriguing to the mathematical scientists, offering challenges on several fronts: mathematical modeling, devising appropriate asymptotic and computational methods, and developing sound mathematical theories. Papers in this volume describe how all of these challenges have been met for particular examples within a number of common combustion scenarios: reactive shocks, low mach number premixed reactive flow, nonpremixed phenomena, and solid propellants. The types of phenomena they examine are also diverse: properties of interfaces and shocks, including curvature effects, the stability and other properties of steady structures, the long time dynamics of evolving solutions, and spatio-temporal patterns. These issues are foremost in combustion research; the papers collected here provide a good representative sampling of contemporary activity in this field.

Inhalt
Bifurcation, pattern formation and chaos in combustion.- Mathematical investigation of the cold boundary difficulty in flame propagation theory.- Nonlinear development of low frequency one-dimensional instabilities for reacting shock waves.- Dynamics of laminar triple-flamelet structures in non-premixed turbulent combustion.- Free boundary problems and dynamical geometry associated with flames.- On the dynamics of weakly curved detonations.- Simplified equations for low mach number combustion with strong heat release.- Attractors and turbulence for some combustion models.- Linear stability of one-dimensional detonations.- Discrete modeling of beds of propellant exposed to strong stimulus.