Modeling flare profiles from relativistic sources

We model time profiles of hares produced by synchrotron mechanism in thin s hells which propagate at relativistic speeds. We derive the flare profiles by computing evolution of energy distribution of electrons from kinetic equ ation and integrating the produced radiation over the surfaces of the const ant arrival time. We show the dependence of flare profiles on: (i) the relative distance rang e of injection of relativistic electrons; (ii) and on the injection time pr ofiles. We also demonstrate time evolution of the spectrum, showing spectra l effects due to adiabatic losses and due to minimum electron injection ene rgy.