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We consider a simplified model for the dynamics of one-dimensionaldetonations with generic losses. It consists of a single partial differentialequation that reproduces, at a qualitative level, the essential properties ofunsteady detonation waves, including pulsating and chaotic solutions. Inparticular, we investigate the effects of shock curvature and friction losseson detonation dynamics. To calculate steady-state solutions, a novel approachto solving the detonation eigenvalue problem is introduced that avoids thewell-known numerical difficulties associated with the presence of a sonicpoint. By using unsteady numerical simulations of the simplified model, we alsoexplore the nonlinear stability of steady-state or quasi-steady solutions.

Qualitative modeling of the dynamics of detonations with losses