Oleinik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit
Coclite GM, Colombo M, Crippa G, De Nitti N, Keimer A, Marconi E, Pflug L, Spinolo LV (2024)
Publication Language: English
Publication Type: Journal article
Publication year: 2024
Journal
Book Volume: 21
Pages Range: 681-705
Journal Issue: 3
DOI: 10.1142/S021989162440006X
Abstract
We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term W:=ퟙ(−∞,0](⋅)exp(⋅)∗ρ" role="presentation">W:=𝟙(−∞,0](⋅)exp(⋅)∗ρ satisfy an Oleĭnik-type entropy condition. More precisely, under different sets of assumptions on the velocity function V" role="presentation">V, we prove that W" role="presentation">W satisfies a one-sided Lipschitz condition and that V′(W)W∂xW" role="presentation">V'(W)W∂xW 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.
Authors with CRIS profile
Nicola De Nitti
Alexander Keimer Professur für Mathematik (Analysis) Lukas Pflug FAU Competence Center Scientific Computing (FAU CSC)
Alexander Keimer Professur für Mathematik (Analysis) Lukas Pflug FAU Competence Center Scientific Computing (FAU CSC)
Involved external institutions
Politecnico di Bari
Italy (IT)
École Polytechnique Fédérale de Lausanne (EPFL)
Switzerland (CH)
University of Padua / Universita degli Studi di Padova
Italy (IT)
Istituto di Matematica Applicata e Tecnologie Informatiche "Enrico Magenes" (IMATI, IMATI-CNR) / Institute of Applied Mathematics and Information Technologies "Enrico Magenes"
Italy (IT)
Universität Basel
Switzerland (CH)
Italy (IT)
École Polytechnique Fédérale de Lausanne (EPFL)
Switzerland (CH)
University of Padua / Universita degli Studi di Padova
Italy (IT)
Istituto di Matematica Applicata e Tecnologie Informatiche "Enrico Magenes" (IMATI, IMATI-CNR) / Institute of Applied Mathematics and Information Technologies "Enrico Magenes"
Italy (IT)
Universität Basel
Switzerland (CH)
How to cite
APA:
Coclite, G.M., Colombo, M., Crippa, G., De Nitti, N., Keimer, A., Marconi, E.,... Spinolo, L.V. (2024). Oleinik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit. Journal of Hyperbolic Differential Equations, 21(3), 681-705. https://doi.org/10.1142/S021989162440006X
MLA:
Coclite, Giuseppe Maria, et al. "Oleinik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit." Journal of Hyperbolic Differential Equations 21.3 (2024): 681-705.
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