A solution is obtained to the problem of determining the conditions of hydrodynamic stability in the presence of flow of gaseous combustion products over the propellant gasification surface. The cross-flow has a small gradient along the direction of motion. Analysis of the obtained dispersion equation shows that hydrodynamic instability with oscillations develops. The transfer coefficients of natural turbulence are represented as the sum of two terms: the first is responsible for the transfer in the absence of cross-flow, and the second takes into account the enhancement of transport processes in the case of cross-flow. Their dependence on the initial temperature of solid propellant combustion predicts a reduction in the negative erosion effect in accordance with experimental data. Accounting for the relaxation time of the evaporation process has a stabilizing effect. In the limit of strong relaxation, this leads to oscillatory stability (in the absence of crossflow) where the perturbations neither grow nor decay. However, arbitrarily weak cross-flow leads to instability.
