On the singular limit problem for nonlocal conservation laws: A general approximation result for kernels with fixed support

Keimer A, Pflug L (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Journal of Mathematical Analysis and Applications Elsevier

Book Volume: 547

Article Number: 129307

Journal Issue: 2

DOI: 10.1016/j.jmaa.2025.129307

Abstract

We prove convergence of solutions of nonlocal conservation laws to their local entropic counterpart for a fundamentally extended class of nonlocal kernels when these kernels approach a Dirac distribution. The nonlocal kernels are assumed to have fixed support and do not have to be monotonic. With sharp estimates of the nonlocal kernels and a surrogate nonlocal quantity, we prove compactness in C(Lloc¹) which allow passing to the limit in the weak formulation. A careful analysis of the entropy condition of local conservation laws together with the named estimators for the considered kernels enable it to prove the entropy admissibility of the nonlocal equation in the limit, completing the convergence proof.

Authors with CRIS profile

Alexander Keimer Lehrstuhl für Analysis Lukas Pflug Sonderforschungsbereich 814/3 Additive Fertigung

How to cite

APA:

Keimer, A., & Pflug, L. (2025). On the singular limit problem for nonlocal conservation laws: A general approximation result for kernels with fixed support. Journal of Mathematical Analysis and Applications, 547(2). https://doi.org/10.1016/j.jmaa.2025.129307

MLA:

Keimer, Alexander, and Lukas Pflug. "On the singular limit problem for nonlocal conservation laws: A general approximation result for kernels with fixed support." Journal of Mathematical Analysis and Applications 547.2 (2025).

BibTeX: Download