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The focus of this minisymposium will be high temperature reactive systems arising in the study of high- and low-speed combustion. The primary purpose is to bring together a number of experts in ordinary and partial differential equations, modellers from combustion theory, and scientific computing specialists to discuss and share ideas for mathematically-analytically and numerically --studying the various combustion models. The emphasis will be on reviewing the field, recent progress, and areas ripe for development.

Combustion science provides a rich source for challenging issues in modelling and scientific computing, raising very difficult mathematical questions. Such questions include: problems of well-posedness which often requires devising new numerical strategies, derivation and validation of asymptotic models, and qualitative behavior studies such as singularity formation and instabilities. Any listing of topics is far from exhaustive.

Understanding such problems provides valuable information to both the combustion science and mathematics communities. Much progress has been made in recent years. For example, the treatment of the reaction-diffusion systems modelling low-speed flames is now almost complete. Major progress has been accomplished in the understanding for new kinds of multidimensional free boundary problems, and singular perturbation techniques have unravelled many intricacies of deflagration and detonation structures including their stability properties. Significant steps have also been taken in understanding models involving complex chemistry. But as more sophisticated modeling evolves, new problems ready for development emerge.

The idea of this conference is therefore to highlight those combustion models that appear both practically interesting and ripe for mathematical development.

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