Dependence of Qualitative Behavior of the Numerical Solutions on the Ignition Temperature for a Combustion Model

Abstract

We study the dependence of qualitative behavior of the numerical solutions (obtained by a projective and upwind finite difference scheme) on the ignition temperature for a combustion model problem with general initial condition. Convergence to weak solution is proved under the Courant-Friedrichs-Lewy condition. Some conditions on the ignition temperature are given to guarantee the solution containing a strong detonation wave or a weak detonation wave. Finally, we give some numerical examples which show that a strong detonation wave can be transformed to a weak detonation wave under some well-chosen ignition temperature.