Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: application to the nonlinearly damped p-system

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dc.contributor.authorCrin-Barat, Timothée
dc.contributor.authorShou, Ling-Yun
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2025-12-05T11:33:24Z
dc.date.available2025-12-05T11:33:24Z
dc.date.issued2025-09-01
dc.date.updated2025-12-05T11:33:24Z
dc.description.abstractA new framework to obtain time-decay estimates for partially dissipative hyperbolic systems set on the real line is developed. Under the classical Shizuta–Kawashima (SK) stability condition, equivalent to the Kalman rank condition in control theory, the solutions of these systems decay exponentially in time for high frequencies and polynomially for low ones. This allows us to derive a sharp description of the space-time decay of solutions for large time. However, such analysis relies heavily on the use of the Fourier transform, which we avoid here, developing the “physical space version” of the hyperbolic hypocoercivity approach introduced in Beauchard and Zuazua [Arch. Ration. Mech. Anal. 199 (2011), 177–227], to prove new asymptotic results in the linear and nonlinear settings. The new physical space version of the hyperbolic hypocoercivity approach allows us to recover the natural heat-like time decay of solutions under sharp rank conditions, without employing Fourier analysis or L1 assumptions on the initial data. Taking advantage of this Fourier-free framework, we establish new enhanced time-decay estimates for initial data belonging to weighted Sobolev spaces. These results are then applied to the nonlinear compressible Euler equations with linear damping. We also prove the logarithmic stability of the nonlinearly damped p-system.en
dc.description.sponsorshipT. Crin-Barat and E. Zuazua have been funded by the Alexander von Humboldt- Professorship program and the Transregio 154 Project “Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks” of the DFG. E. Zuazua has been funded by the ModConFlex Marie Curie Action, HORIZON-MSCA-2021-DN-01, the COST Action MAT-DYN-NET, grants PID2020-112617GB-C22 and TED2021-131390B-I00 of MINECO (Spain), and by the Madrid Government – UAMAgreement for the Excellence of the University Research Staff in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). L.-Y. Shou is supported by the National Natural Science Foundation of China (12301275) and the China Postdoctoral Science Foundation (2023M741694)en
dc.identifier.citationCrin-Barat, T., Shou, L.-Y., & Zuazua, E. (2025). Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: application to the nonlinearly damped p-system. Annales de l’Institut Henri Poincare (C) Analyse Non Lineaire, 42(5), 1165-1218. https://doi.org/10.4171/AIHPC/128
dc.identifier.doi10.4171/AIHPC/128
dc.identifier.eissn1873-1430
dc.identifier.issn0294-1449
dc.identifier.urihttps://hdl.handle.net/20.500.14454/4539
dc.language.isoeng
dc.publisherEuropean Mathematical Society Publishing House
dc.rights©2024 Association Publications de l’Institut Henri Poincaré
dc.subject.otherAsymptotic analysis
dc.subject.otherHypocoercivity
dc.subject.otherNonlinear damping
dc.subject.otherPartially dissipative hyperbolic systems
dc.subject.otherTime-weighted estimates
dc.titleLarge time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: application to the nonlinearly damped p-systemen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.endPage1218
oaire.citation.issue5
oaire.citation.startPage1165
oaire.citation.titleAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
oaire.citation.volume42
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
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