The paper studies uncertaintly quantification for evolution equations with various time-dependent parameters that evolve as stochastic processes. Instead of a sensitivity analysis, we measure functionals of the solution, the so-called quantities of interest, by involving scalarizing statistics. The nested distance respects the evolutionary aspect of the problem at hand. Motivated by applications in pedestrian dynamics, we apply these results to drift-diffusion equations in the case when the total mass is−due to boundary or reaction terms−not conserved. We first provide existence and stability for the deterministic problem and then involve uncertainty in the data, which results in Lipschitz continuity with respect to the nested distance. Finally, we present a numerical study illustrating these findings.

中文翻译：

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漂移扩散方程的不确定性分析

我们研究各种参数随机时的漂移扩散型演化方程。受行人动力学应用的启发，我们关注总质量由于边界或反应项而不守恒的情况。在提供确定性问题的存在性和稳定性后，我们考虑数据的不确定性。我们建议通过标量化统计来衡量解决方案的函数，即所谓的感兴趣量 (QoI)，而不是敏感性分析。对于这些汇总统计数据，我们提供概率连续性结果。