Fundamental Mathematical Theory for Thermal Explosions in Rigid Solids and in Gases.

摘要

This research project has emphasized the formulation of rational mathematical models for transient and steady combustion processes. In particular thermal explosion, shock wave initiation and high speed combustion waves have been examined. In each case the describing mathematical system is analyzed using both formal and constructive techniques. The former are employed to consider issues of existence and uniqueness, solution bounds and general trajectory properties. Constructive solution development is based on a combination of asymptotic and numerical methods. This hybrid approach to the study of combustion problems has permitted us to develop both a rigorous and quantitative understanding of complex, initial-boundary value problems. Keywords: Thermal explosion; combustion; flames; deflagrations; reactive gas dynamics.