Linear inelastic kinetic equations modelling the spread of fake news and its interplay with personal awareness
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911218687541248 |
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| author | Fraia, Martina Loy, Nadia Tosin, Andrea |
| author_facet | Fraia, Martina Loy, Nadia Tosin, Andrea |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_01965 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear inelastic kinetic equations modelling the spread of fake news and its interplay with personal awareness Fraia, Martina Loy, Nadia Tosin, Andrea Physics and Society 35Q20, 35Q70, 35Q91, 91D30 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. |
| title | Linear inelastic kinetic equations modelling the spread of fake news and its interplay with personal awareness |
| topic | Physics and Society 35Q20, 35Q70, 35Q91, 91D30 |
| url | https://arxiv.org/abs/2501.01965 |