2024/09/01 by Giuseppe Maria Coclite, Maria Colombo, Gianluca Crippa +5 · 7 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Applied mathematics #Biology #Classical mechanics #Conservation law #Law #Limit (mathematics) #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Physics #Political science #Stability and Controllability of Differential Equations #Type (biology)
paper · doi:10.1142/s021989162440006x
published in Journal of Hyperbolic Differential Equations 21(03), 681-705 (World Scientific)
crossref issued 2024/09/01 · crossref published 2024/09/01 · crossref published-print 2024/09/01 · openalex publication_date 2024/09/01 · crossref created 2025/01/23 · crossref deposited 2025/01/23 · crossref published-online 2025/01/24 · openalex created_date 2025/01/24 · openalex updated_date 2026/08/06 · crossref indexed 2026/08/06
We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term [Formula: see text] satisfy an Oleĭnik-type entropy condition. More precisely, under different sets of assumptions on the velocity function [Formula: see text], we prove that [Formula: see text] satisfies a one-sided Lipschitz condition and that [Formula: see text] satisfies a one-sided bound, respectively. As a byproduct, we deduce that, as the exponential kernel is rescaled to converge to a Dirac delta distribution, the weak solution of the nonlocal problem converges to the unique entropy-admissible solution of the corresponding local conservation law, under the only assumption that the initial datum is essentially bounded and not necessarily of bounded variation.