Existence result for a two-dimensional system of conservation laws with unilateral constraints. (July 2023)

• Record Type: Journal Article
• Authors: Berthelin, F.
• Is Part Of: Nonlinear analysis. Volume 232(2023)
• Publication Date: 2023-07
• Subjects: 35L87 -- 35L65 -- 76N10 -- 35A35 -- 35D30 -- 76T10; Conservation laws with constraint -- Pressureless gas -- Sticky blocks -- Splitting dynamics -- Pedestrian flow; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2023.113248
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The aim of this paper is to study a pressureless model with unilateral constraint in two dimensions. The corresponding one-dimensional case is a traffic flow model and was studied in Berthelin et al. (2008). The two-dimensional extension is linked to a pedestrian flow. Several challenges, geometric and analytical, appear with respect to the one-dimensional case. We get the existence of weak solutions for general initial data and the constraints taken in the strong sense.