a) Evolution with time of the radii of the SNR/ISM forward shock (black solid line), SNR/bubble contact discontinuity (red dashed line), and bubble reverse shock (blue dotted line). The CD radius becomes larger than the SNR shock radius, which indicates that the model adopted here does not apply after a few  × 10⁵ yr. b) Evolution with time of the radii of the bubble/ISM forward (black solid line) and reverse shocks (blue dotted line).