Riemann problems with non--local point constraints and capacity drop
In the present note we discuss in details the Riemann problem for a one-dimensional hyperbolic conservation law subject to a point constraint. We investigate how the regularity of the constraint operator impacts the well--posedness of the problem, namely in the case, relevant for numerical applicati...
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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.2015.12.259 |
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| author | Boris Andreianov Carlotta Donadello Ulrich Razafison Massimiliano D. Rosini |
| author_facet | Boris Andreianov Carlotta Donadello Ulrich Razafison Massimiliano D. Rosini |
| author_sort | Boris Andreianov |
| collection | DOAJ |
| description | In the present note we discuss in details the Riemann problem for a one-dimensional hyperbolic conservation law subject to a point constraint. We investigate how the regularity of the constraint operator impacts the well--posedness of the problem, namely in the case, relevant for numerical applications, of a discretized exit capacity. We devote particular attention to the case in which the constraint is given by a non--local operator depending on the solution itself. We provide several explicit examples. We also give the detailed proof of some results announced in the paper [Andreianov, Donadello, Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop], which is devoted to existence and stability for a more general class of Cauchy problems subject to Lipschitz continuous non--local point constraints. |
| format | Article |
| id | doaj-art-5e6272bd36854e97867aafd3023b7162 |
| 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-5e6272bd36854e97867aafd3023b71622025-01-24T02:31:45ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-0112225927810.3934/mbe.2015.12.259Riemann problems with non--local point constraints and capacity dropBoris Andreianov0Carlotta Donadello1Ulrich Razafison2Massimiliano D. Rosini3Laboratoire de Mathématiques CNRS UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon CedexLaboratoire de Mathématiques CNRS UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon CedexLaboratoire de Mathématiques CNRS UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon CedexICM, Uniwersytet Warszawski, ul. Prosta 69, 00838 WarsawIn the present note we discuss in details the Riemann problem for a one-dimensional hyperbolic conservation law subject to a point constraint. We investigate how the regularity of the constraint operator impacts the well--posedness of the problem, namely in the case, relevant for numerical applications, of a discretized exit capacity. We devote particular attention to the case in which the constraint is given by a non--local operator depending on the solution itself. We provide several explicit examples. We also give the detailed proof of some results announced in the paper [Andreianov, Donadello, Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop], which is devoted to existence and stability for a more general class of Cauchy problems subject to Lipschitz continuous non--local point constraints.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.259loss of uniquenessriemann problemcrowd dynamicsloss of self--similaritycapacity drop.non--local constrained hyperbolic pde's |
| spellingShingle | Boris Andreianov Carlotta Donadello Ulrich Razafison Massimiliano D. Rosini Riemann problems with non--local point constraints and capacity drop Mathematical Biosciences and Engineering loss of uniqueness riemann problem crowd dynamics loss of self--similarity capacity drop. non--local constrained hyperbolic pde's |
| title | Riemann problems with non--local point constraints and capacity drop |
| title_full | Riemann problems with non--local point constraints and capacity drop |
| title_fullStr | Riemann problems with non--local point constraints and capacity drop |
| title_full_unstemmed | Riemann problems with non--local point constraints and capacity drop |
| title_short | Riemann problems with non--local point constraints and capacity drop |
| title_sort | riemann problems with non local point constraints and capacity drop |
| topic | loss of uniqueness riemann problem crowd dynamics loss of self--similarity capacity drop. non--local constrained hyperbolic pde's |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.259 |
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