Well-posedness of IBVP for 1D scalar non-local conservation laws

Paola Goatin (1) , Elena Rossi (1)

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

We consider the initial boundary value problem (IBVP) for a non-local scalar conservation laws in one space dimension. The non-local operator in the flux function is not a mere convolution product, but it is assumed to be aware of boundaries. Introducing an adapted Lax-Friedrichs algorithm, we provide various estimates on the approximate solutions that allow to prove the existence of solutions to the original IBVP. The uniqueness follows from the Lipschitz continuous dependence on initial and boundary data, which is proved exploiting results available for the local IBVP.

Mots clés: Initial-boundary value problem; Scalar conservation laws; Non-local flux; Lax-Friedrichs scheme

Domaines: Equations aux dérivées partielles [math.AP]

Paola Goatin, Elena Rossi. Well-posedness of IBVP for 1D scalar non-local conservation laws. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2019, 99 (11), ⟨10.1002/zamm.201800318⟩. ⟨hal-01929196⟩