A mixed system modeling two-directional pedestrian flows
In this article, we present a simplified model to describe the dynamics of two groups of pedestrians moving in opposite directions in a corridor.The model consists of a $2\times 2$ system of conservation laws of mixed hyperbolic-elliptic type.We study the basic properties of the system to understand...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.375 |
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| author | Paola Goatin Matthias Mimault |
| author_facet | Paola Goatin Matthias Mimault |
| author_sort | Paola Goatin |
| collection | DOAJ |
| description | In this article, we present a simplified model to describe the dynamics of two groups of pedestrians moving in opposite directions in a corridor.The model consists of a $2\times 2$ system of conservation laws of mixed hyperbolic-elliptic type.We study the basic properties of the system to understand why and how bounded oscillations in numerical simulations arise.We show that Lax-Friedrichs scheme ensures the invariance of the domain and we investigate the existence of measure-valued solutionsas limit of a subsequence of approximate solutions. |
| format | Article |
| id | doaj-art-a825527533064b87bc1a33d64aa00708 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a825527533064b87bc1a33d64aa007082025-01-24T02:31:45ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-0112237539210.3934/mbe.2015.12.375A mixed system modeling two-directional pedestrian flowsPaola Goatin0Matthias Mimault1INRIA Sophia Antipolis - Méditerranée, EPI OPALE, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis CedexINRIA Sophia Antipolis - Méditerranée, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis CedexIn this article, we present a simplified model to describe the dynamics of two groups of pedestrians moving in opposite directions in a corridor.The model consists of a $2\times 2$ system of conservation laws of mixed hyperbolic-elliptic type.We study the basic properties of the system to understand why and how bounded oscillations in numerical simulations arise.We show that Lax-Friedrichs scheme ensures the invariance of the domain and we investigate the existence of measure-valued solutionsas limit of a subsequence of approximate solutions.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.375macroscopic models for pedestrian flowssystems of conservation lawsfinite volume schemesmixed hyperbolic-elliptic systemsyoung measures. |
| spellingShingle | Paola Goatin Matthias Mimault A mixed system modeling two-directional pedestrian flows Mathematical Biosciences and Engineering macroscopic models for pedestrian flows systems of conservation laws finite volume schemes mixed hyperbolic-elliptic systems young measures. |
| title | A mixed system modeling two-directional pedestrian flows |
| title_full | A mixed system modeling two-directional pedestrian flows |
| title_fullStr | A mixed system modeling two-directional pedestrian flows |
| title_full_unstemmed | A mixed system modeling two-directional pedestrian flows |
| title_short | A mixed system modeling two-directional pedestrian flows |
| title_sort | mixed system modeling two directional pedestrian flows |
| topic | macroscopic models for pedestrian flows systems of conservation laws finite volume schemes mixed hyperbolic-elliptic systems young measures. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.375 |
| work_keys_str_mv | AT paolagoatin amixedsystemmodelingtwodirectionalpedestrianflows AT matthiasmimault amixedsystemmodelingtwodirectionalpedestrianflows AT paolagoatin mixedsystemmodelingtwodirectionalpedestrianflows AT matthiasmimault mixedsystemmodelingtwodirectionalpedestrianflows |