Aims: Drawing an analogy with Active Galactic Nuclei, we investigate the one-zone SSC model of Gamma Ray Bursts afterglows in the presence of electron injection and cooling both by synchrotron and SSC losses. Methods: We solve the spatially averaged kinetic equations which describe the simultaneous evolution of particles and photons, obtaining the multi-wavelength spectrum as a function of time. We back up our numerical calculations with analytical solutions of the equations using various profiles of the magnetic field evolution under certain simplifying assumptions. Results: We apply the model to the afterglow evolution of GRBs in a uniform density environment and examine the impact various parameters have on the multiwavelength spectra. We find that in cases where the electron injection and/or the ambient density is high, the losses are dominated by SSC and the solutions depart significantly from the ones derived in the synchrotron standard cases.
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