This dissertation formulates a one-dimensional model for pulse combustion and addresses the problem of existence of a unique solution for the resulting mixed hyperbolic-parabolic initial-boundary value problem. There have been no known attempts to mathematically analyze models associated with pulse combustion that take into account spatial dependence; in particular, the existence and uniqueness of solutions of the relevant initial-boundary value problems associated with such models has not been addressed. Moreover, the initial-boundary value problems associated with pulse combustion modeling differ from the majority of the gas-dynamics related initial boundary-value problems in the literature; they are often defined on a bounded domain and lead to situations involving time-dependent boundary conditions. These considerations are not unique to pulse combustor modeling; analogous initial-boundary value problems arise in many other physical applications. Therefore the mathematical analysis presented in this thesis may be of some significance for other physical problems as well.