On the singular limit problem for a discontinuous nonlocal conservation law

Keimer A, Pflug L (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Nonlinear Analysis - Theory Methods & Applications Elsevier

Book Volume: 237

Article Number: 113381

DOI: 10.1016/j.na.2023.113381

Abstract

In this contribution, we study the singular limit problem of a nonlocal conservation law with a discontinuity in space. The corresponding local equation can be transformed diffeomorphically to a classical scalar conservation law to which the well-known Kružkov theory can be applied. However, the nonlocal equation does not scale that way, which is why the study of convergence is interesting to pursue. For exponential kernels in the nonlocal operator, we establish convergence to the solution of the corresponding local equation under mild conditions on the discontinuous velocity. We illustrate our results with some numerical examples.

Authors with CRIS profile

Alexander Keimer Department Mathematik Lukas Pflug Sonderforschungsbereich 814/3 Additive Fertigung

How to cite

APA:

Keimer, A., & Pflug, L. (2023). On the singular limit problem for a discontinuous nonlocal conservation law. Nonlinear Analysis - Theory Methods & Applications, 237. https://dx.doi.org/10.1016/j.na.2023.113381

MLA:

Keimer, Alexander, and Lukas Pflug. "On the singular limit problem for a discontinuous nonlocal conservation law." Nonlinear Analysis - Theory Methods & Applications 237 (2023).

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