Thermal stability of a disturbed fluid flow

Stability of periodic solutions of a non-self-similar nonlinear problem is studied. The problem describes the thermal state of an axial fluid flow with continuously distributed sources of heat. The flow experiences the action of external low-amplitude perturbations changing in time in accordance with known periodic laws. The spectral problem is solved by the method of parametrix, and the critical conditions of the thermal explosion are determined in the linear approximation. Stability of the periodic solution at the critical point is evaluated using the known theorem of factorization, which takes into account the effect of nonlinear terms of the heat-balance equation. The calculation results show that the periodic solution is stable if the total action of external periodic perturbations at the critical point is directed to reduction of the fluid-flow temperature.