Singular limit for nonlocal conservation laws with non-locality in density and velocity

Immanuel Ben Porat

Singular limit for nonlocal conservation laws with non-locality in density and velocity

Analysis of PDEs 2026-07-15 v1

Authors: Immanuel Ben Porat

Abstract

We study the singular limit of a nonlocal conservation law incorporating both non-locality in density and velocity. We derive classical solutions of the underlying Burgers equation as a singular limit. The derivation is valid up until the maximal time before formation of shocks. The main result answers a question raised in [10].

Keywords

nonlocal conservation laws singular limit Burgers equation nonlocality in density nonlocality in velocity shock formation

Cite

@article{arxiv.2607.14002,
  title  = {Singular limit for nonlocal conservation laws with non-locality in density and velocity},
  author = {Immanuel Ben Porat},
  journal= {arXiv preprint arXiv:2607.14002},
  year   = {2026}
}

Comments

8 pages