Abstract: By using prior estimates and differential inequality technique, the author discussed the influence of base perturbations on the stability of heat conduction inside a semi infinite cylinder. The author proves that as the disturbance amplitude decreases, the solution converges exponentially to the solution corresponding to a completely flat base. This result has certain theoretical significance for  the robustness of heat conduction model and the potential impact of small geometric irregularities on heat transfer prediction.

Key words: a priori bound, disturbance parameter, structural stability, continuous dependence