Stability estimates for non-local scalar conservation laws. (February 2019)

• Record Type: Journal Article
• Authors: Chiarello, Felisia Angela; Goatin, Paola; Rossi, Elena
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 668
• Page End: 687
• Publication Date: 2019-02
• Subjects: Scalar conservation laws -- Non-local flux -- Stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.07.027
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We prove the stability of entropy weak solutions of a class of scalar conservation laws with non-local flux arising in traffic modelling. We obtain an estimate of the dependence of the solution with respect to the kernel function, the speed and the initial datum. Stability is obtained from the entropy condition through doubling of variable technique. We finally provide some numerical simulations illustrating the dependencies above for some cost functionals derived from traffic flow applications.