标题： 线性非弹性动力学方程：建模假新闻的传播及其与个人意识的相互作用 显示英文标题

标题： Linear inelastic kinetic equations modelling the spread of fake news and its interplay with personal awareness

摘要： 本文介绍了一个描述学习过程的动理学模型，该过程引导个体形成关于假新闻的个人意识。接着，我们将此模型的结果嵌入到另一个动理学模型中，该模型描述了社交网络上新闻受欢迎程度的变化，这取决于传播信息的可靠性。这两个模型均以线性非弹性Boltzmann型方程的形式表述，我们通过广泛使用傅里叶方法来研究这些方程的主要分析性质——解的存在性和唯一性、趋向平衡的趋势以及平衡分布的识别。此外，我们还利用Monte Carlo数值模拟验证了这些分析结果。 显示英文摘要

摘要： In this paper, we introduce a kinetic model which describes a learning process leading individuals to build personal awareness about fake news. Next, we embed the results of this model into another kinetic model, which describes the popularity gained by news on social media conditioned to the reliability of the disseminated information. Both models are formulated in terms of linear inelastic Boltzmann-type equations, of which we investigate the main analytical properties - existence and uniqueness of solutions, trend to equilibrium, identification of the equilibrium distributions - by employing extensively Fourier methods for kinetic equations. We also provide evidence of the analytical results by means of Monte Carlo numerical simulations.