UHECR spectral densities of a GRB source in the optically thick scenario. Shaded regions and line styles indicate the effect of different model assumptions. Left: Influence of a time-varying injection with a fixed total injection. The case of a constant injection (solid lines) is contrasted with a quadratically increasing injection (dotted bound) and a linearly decreasing injection (dash-dotted bound). Right: Influence of rigidity-dependent escape assumptions. The solid lines represent advective escape, as in the left figure. The dash-dotted lines show the Bohmian diffusion, and the dotted lines show the effect of diffusion under a Kolmogorov-distributed turbulent magnetic field. Additional details are given in the text and in Appendix D.