A brief overview of existence results and decay time estimates for a mathematical modeling of scintillating crystals

Inorganic scintillating crystals can be modelled as continua with microstructure. For rigid and isothermal crystals, the evolution of charge carriers becomes in this way described by a reaction-diffusion-drift equation coupled with the Poisson equation of electrostatic. Here, we give a survey of the available existence and asymptotic decays results for the resulting boundary value problem, the latter being a direct estimate of the scintillation decay time. We also show how to recover various approximated models which encompass also the two most used phenomenological models for scintillators, namely, the kinetic and diffusive ones. Also for these cases, we show, whenever it is possible, which existence and asymptotic decays estimate results are known to date.