General stability estimates in nonlocal traffic models for several populations

• DOI: 10.1007/s00030-025-01034-w
• Publication Date: 2025-02-25T16:25:21Z
• Authors: Rinaldo M. Colombo; Mauro Garavello; Claudia Nocita
• Keywords: Mathematics - Analysis of PDEs; 35L65, 76A30, 65M22; Nonlocal conservation laws; Multipopulation traffic modeling; Nonlocal traffic modeling; FOS: Mathematics; Analysis of PDEs (math.AP)

Abstract We prove global existence, uniqueness and

$$\textrm{L}^1$$

L 1

stability of solutions to general systems of nonlocal conservation laws modeling multiclass vehicular traffic. Each class follows its own speed law and has specific effects on the other classes’ speeds. Moreover, general explicit dependencies of the speed laws on space and time are allowed. Solutions are proved to depend continuously—in suitable norms—on all terms appearing in the equations, as well as on the initial data. Numerical simulations show the relevance and the effects of the nonlocal terms.