Based on the OpenFOAM platform, a numerical study was conducted to investigate the propagation characteristics of a detonation wave in uniformly premixed gases within a semi-confined channel, specifically examining the changes in wave's structure and analyzing the detonation reinitiation-extinguishment process. The results indicate that, due to the weak confinement, the detonation wave experiences lateral expansion, with transverse waves on the detonation wave front penetrating into the inert gas and forming segmented protrusions on the oblique shock wave. During the propagation process, the number of transverse waves decreases gradually, and the reflected waves formed by the interaction between transverse waves and the inert gas are weak, collectively leading to a gradual decay in the strength of the detonation wave and a reduction in the frequency of pressure oscillation on the detonation wave front. Furthermore, when transverse waves interact with the inert gas and undergo Mach reflection, the reflected waves would detach the inert gas and form new transverse waves promoted by upward-moving old transverse waves and disturbances on the flame front, thereby extending the duration distance of the detonation wave. Subsequently, after the detonation wave decouples, a transverse wave reflected from the inert gas interface interacts with the lower wall, triggering local detonation reinitiation, which generates a higher-intensity longitudinal wave that couples with the leading shock wave, temporarily restoring the detonation wave and forming lateral detonation in the decoupled region. However, the detonation wave will ultimately extinguish due to the attenuation of transverse waves' intensity and decreasing number of these waves.