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

Nonlinearity Institute of Physics: Hybrid Open Access

URI: https://iopscience.iop.org/article/10.1088/1361-6544/acf01d

DOI: 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 Department Mathematik Lukas Pflug Lehrstuhl für Angewandte Mathematik Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Polytechnic University of Bari

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://dx.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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