Stability of the combustion wave in a viscoelastic medium to small one-dimensional perturbations

The problem of stability of the conversion front in a viscoelastic medium is formulated. The stability study is performed by the method of small perturbations. Nonlinear equations are derived for decrements of decay and complex frequency. Several particular cases are analyzed. A significant effect of the time of relaxation of viscous stresses on the flammability limits for both high-velocity and low-velocity regimes is demonstrated.