Skip to Main content Skip to Navigation
Journal articles

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

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download

https://hal.inria.fr/hal-01929196
Contributor : Elena Rossi <>
Submitted on : Wednesday, November 21, 2018 - 9:27:15 AM
Last modification on : Thursday, May 20, 2021 - 9:12:01 AM
Long-term archiving on: : Friday, February 22, 2019 - 1:07:03 PM

Files

ibvp2.pdf
Files produced by the author(s)

Identifiers

Citation

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, Wiley-VCH Verlag, 2019, 99 (11), ⟨10.1002/zamm.201800318⟩. ⟨hal-01929196⟩

Share

Metrics

Record views

316

Files downloads

204