Long-time convergence of a nonlocal Burgers' equation towards the local N-wave
Coclite GM, De Nitti N, Keimer A, Pflug L, Zuazua Iriondo E (2023)
Publication Language: English
Publication Status: Accepted
Publication Type: Journal article, Online publication
Future Publication Type: Journal article
Publication year: 2023
Journal
URI: https://iopscience.iop.org/article/10.1088/1361-6544/acf01d
Open Access Link: https://cvgmt.sns.it/paper/5930/
Abstract
We study the long-time behavior of the unique weak solution of a nonlocal regularization of the (inviscid) Burgers' equation where the velocity is approximated by a one-sided convolution with an exponential kernel. The initial datum is assumed to be positive, bounded, and integrable. The asymptotic profile is given by the "N -wave'' entropy solution of the Burgers' equation. The key ingredients of the proof are a suitable scaling argument and a nonlocal Oleinik-type estimate.
Authors with CRIS profile
Nicola De Nitti
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Alexander Keimer
Professur für Mathematik (Analysis)
Lukas Pflug
Lehrstuhl für Angewandte Mathematik
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Additional Organisation(s)
Involved external institutions
Italy (IT)How to cite
APA:
Coclite, G.M., De Nitti, N., Keimer, A., Pflug, L., & Zuazua Iriondo, E. (2023). Long-time convergence of a nonlocal Burgers' equation towards the local N-wave. Nonlinearity. https://doi.org/10.1088/1361-6544/acf01d
MLA:
Coclite, Giuseppe Maria, et al. "Long-time convergence of a nonlocal Burgers' equation towards the local N-wave." Nonlinearity (2023).
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