This volume collects the results of a workshop held at Aachen, West-Germany, Oct. 12 - Oct. 14, 1981. The purpose in bringing together scientists actively working in the field of numerical methods in flame propagation was two-fold: 1. To confront them with recent results obtained by large ac­ tivation-energy asymptotics and to check these numerically. 2. To compare different numerical codes and different trans­ port models for flat flame calculations with complex che­ mistry. Two test problems were formulated by the editors to meet these objectives. Test problem A was an unsteady propagating flat flame with one-step chemistry and Lewis number different from unity while test problem B was the steady, stoichiometric hy­ drogen-air flame with prescribed complex chemistry. The parti­ cipants were asked to solve one or both test problems and to present recent work of their own choice at the meeting. The results of the numerical calculations of test problem A are challenging just as much for scientists employing numerical me­ thods as for those devoted to large activation-energy asympto­ tics: Satisfactory agreement between the five different groups were obtained only for two out of six cases, those with Lewis number Le equal to one. The very strong oscillations that oc­ cur at Le = 2 and a nondimensional activation energy of 20 were accurately resolved only by one group. This case is par­ ticular interesting because the asymptotic theory so far pre­ dicts instability but not oscillations.

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.

Addressing various aspects of nonlinear partial differential equations, this volume contains papers and lectures presented at the Congress on Free boundary Problems, Theory and Application held in Zakopane, Poland in 1995. Topics include existence, uniqueness, asymptotic behavior, and regularity of solutions and interfaces.

This volume gathers the contributions of six world experts to a course on combustion modelling. Therefore, a pedagogical effort has been made in writing up these texts, which cover state of the art advances in most aspects of combustion science. The book is aimed at students, researches and engineers, as was the course.