Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave

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dc.contributor.author Coclite, Giuseppe Maria
dc.contributor.authorDe Nitti, Nicola
dc.contributor.authorKeimer, Alexander
dc.contributor.authorPflug, Lukas
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2025-06-06T15:33:33Z
dc.date.available2025-06-06T15:33:33Z
dc.date.issued2023-11-04
dc.date.updated2025-06-06T15:33:33Z
dc.description.abstractWe study the long-time behaviour of the unique weak solution of a nonlocal regularisation 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.en
dc.description.sponsorshipG M Coclite has been partially supported by the Project funded under the National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.4—Call for tender No.3138 of 16 December 2021 of Italian Ministry of University and Research funded by the European Union—NextGenerationEUoAward Number: CN000023, Concession Decree No. 1033 of 17 December 2022 adopted by the Italian Ministry of University and Research, CUP: D93C22000410001, Centro Nazionale per la Mobilit`a Sostenibile and the Italian Ministry of Education, University and Research under the Programme Department of Excellence Legge 232/2016 (Grant No. CUP—D93C23000100001). L Pflug has been supported by the Deutsche Forschungsgemeinschaft (DFG)—Project-ID 41 622 9255—SFB 1411. E Zuazua has been funded by the Alexander von Humboldt-Professorship program, the ModConFlex Marie Curie Action, HORIZON-MSCA-2021-DN-01, the COST Action MAT-DYN-NET, the Transregio 154 Project ‘Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks’ of the DFG, Grants PID2020-11 2617GBC22 and TED2021-13 1390B-I00 of MINECO (Spain), and by the Madrid Goverment—UAM Agreement for the Excellence of the University Research Staff in the context of the V PRICIT (Regional Programme of Research and Technological Innovation)en
dc.identifier.citationCoclite, G. M., De Nitti, N., Keimer, A., Pflug, L., & Zuazua, E. (2023). Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave. Nonlinearity, 36(11), 5998-6019. https://doi.org/10.1088/1361-6544/ACF01D
dc.identifier.doi10.1088/1361-6544/ACF01D
dc.identifier.eissn1361-6544
dc.identifier.issn0951-7715
dc.identifier.urihttps://hdl.handle.net/20.500.14454/2964
dc.language.isoeng
dc.publisherInstitute of Physics
dc.rights© 2023 IOP Publishing Ltd & London Mathematical Society
dc.subject.other35L65
dc.subject.otherApproximation of local conservation laws
dc.subject.otherBurgers equation
dc.subject.otherEntropy solutions
dc.subject.otherN-waves
dc.subject.otherNonlocal conservation laws
dc.subject.otherNonlocal flux
dc.subject.otherSource-type solutions
dc.titleLong-time convergence of a nonlocal Burgers’ equation towards the local N-waveen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.endPage6019
oaire.citation.issue11
oaire.citation.startPage5998
oaire.citation.titleNonlinearity
oaire.citation.volume36
oaire.licenseConditionhttps://creativecommons.org/licenses/by/3.0
oaire.versionVoR
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