Stability estimates for non-local scalar conservation laws

Felisia Angela Chiarello (1) , Paola Goatin (1) , Elena Rossi (1)

1 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences

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.

Mots clés: Non-local flux; Scalar conservation laws; Stability

Domaines: Equations aux dérivées partielles [math.AP]

Felisia Angela Chiarello, Paola Goatin, Elena Rossi. Stability estimates for non-local scalar conservation laws. Nonlinear Analysis: Real World Applications, 2019, 45, pp.668-687. ⟨10.1016/j.nonrwa.2018.07.027⟩. ⟨hal-01685806⟩