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.

中文翻译：

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闪烁晶体数学建模的存在结果和衰减时间估计的简要概述

无机闪烁晶体可以模拟为具有微观结构的连续体。对于刚性和等温晶体，电荷载流子的演化以这种方式由反应-扩散-漂移方程与静电泊松方程相结合来描述。在这里，我们对所得边界值问题的可用存在性和渐近衰减结果进行了调查，后者是闪烁衰减时间的直接估计。我们还展示了如何恢复各种近似模型，这些模型还包括闪烁体的两个最常用的现象学模型，即动力学模型和扩散模型。同样对于这些情况，我们会尽可能展示迄今为止已知的存在性和渐近衰减估计结果。