English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We consider a class of nonlocal conservation laws with exponential kernel andprove that quantities involving the nonlocal term$W:=\mathbb{1}_{(-\infty,0]}(\cdot)\exp(\cdot) \ast \rho$ satisfy anOle\u{\i}nik-type entropy condition. More precisely, under different sets ofassumptions on the velocity function $V$, we prove that $W$ satisfies aone-sided Lipschitz condition and that $V'(W) W \partial_x W$ satisfies aone-sided bound, respectively. As a byproduct, we deduce that, as theexponential kernel is rescaled to converge to a Dirac delta distribution, theweak solution of the nonlocal problem converges to the uniqueentropy-admissible solution of the corresponding local conservation law, underthe only assumption that the initial datum is essentially bounded and notnecessarily of bounded variation.

Ole\u{\i}nik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit