An existence result for a constrained two-phase transition model with metastable phase for vehicular traffic
| Autor: | Carlotta Donadello, Nikodem Dymski, Massimiliano D. Rosini, Mohamed Benyahia |
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| Přispěvatelé: | Gran Sasso Science Institute (GSSI), Istituto Nazionale di Fisica Nucleare (INFN), Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Instytut Matematyki = Institute of Mathematics [Lublin], Uniwersytet Marii Curie-Sklodowskiej = University Marii Curie-Sklodowskiej [Lublin] (UMCS), Università degli Studi di Ferrara (UniFE) |
| Rok vydání: | 2018 |
| Předmět: |
Phase transition
Lighthill-Whitham-Richards model Phase (waves) Flux Aw–Rascle–Zhang model 01 natural sciences NO Mathematics - Analysis of PDEs Wave-front tracking Intersection Metastability FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Lighthill–Whitham–Richards model Conservation laws Mathematics Cauchy problem Applied Mathematics 010102 general mathematics Mathematical analysis Cauchy distribution [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation Point constraint on the density flux 010101 applied mathematics Constraint (information theory) Phase transitions Analysis Aw-Rascle-Zhang model Bounded function Analysis of PDEs (math.AP) |
| Zdroj: | Nonlinear Differential Equations and Applications NoDEA. 25 |
| ISSN: | 1420-9004 1021-9722 |
| Popis: | In this paper we study a phase transition model for vehicular traffic flows. Two phases are taken into account, according to whether the traffic is light or heavy. We assume that the two phases have a non-empty intersection, the so called metastable phase. The model is given by the Lighthill–Whitham–Richards model in the free-flow phase and by the Aw–Rascle–Zhang model in the congested phase. In particular, we study the existence of solutions to Cauchy problems satisfying a local point constraint on the density flux. We prove that if the constraint F is higher than the minimal flux $$f_\mathrm{c}^-$$ of the metastable phase, then constrained Cauchy problems with initial data of bounded total variation admit globally defined solutions. We also provide sufficient conditions on the initial data that guarantee the global existence of solutions also in the case $$F < f_\mathrm{c}^-$$ . These results are obtained by applying the wave-front tracking technique. |
| Databáze: | OpenAIRE |
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