UAH > Math > Colloquia > 2/26/2008
I consider combustion wavefronts arising in the model for high Lewis number combustion processes such as combustion of high density liquid fuels. An efficient method for the proof of the existence and uniqueness of the combustion front is provided by geometric singular perturbation theory. The fronts supported by the model with very large Lewis numbers are small perturbations of the front supported by the model with the infinite Lewis number. The question of stability of the fronts is more complicated. I will discuss issues and recent results on the stability analysis that arise at both the linear and nonlinear level.