Weakly elliptic damping gives sharp decay

Lassi Paunonen; Nicolas Vanspranghe; Ruoyu P. T. Wang

doi:10.5802/crmath.767

Research article - Partial differential equations

Weakly elliptic damping gives sharp decay

Lassi Paunonen ¹ ; Nicolas Vanspranghe ¹ ; Ruoyu P. T. Wang ²

¹ Mathematics Research Centre, Faculty of Information Technology and Communication Sciences, Tampere University, P.O. Box 692, 33101 Tampere, Finland
² Department of Mathematics, University College London, London, WC1H 0AY, United Kingdom

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 1263-1275

Abstract (Original language)
Résumé

We prove that weakly elliptic damping gives sharp energy decay for the abstract damped wave semigroup, where the damping is not in the functional calculus. In this case, there is no overdamping. We show applications in linearised water waves and Kelvin–Voigt damping.

On démontre qu’un amortissement faiblement elliptique mène à une décroissance optimale de l’énergie pour le semi-groupe d’ondes amorties abstraites associé, et ce, même lorsque cet amortissement n’est pas dans le calcul fonctionnel. Dans ce cas, il n’y pas de suramortissement. On présente des applications à une équation des vagues linéarisée et à l’amortissement de Kelvin–Voigt.

Received: 2024-09-07
Revised: 2025-01-10
Accepted: 2025-06-10
Published online: 2025-10-13

DOI: 10.5802/crmath.767

Classification: 35L05, 47D06

Author's affiliations:

Lassi Paunonen ¹; Nicolas Vanspranghe ¹; Ruoyu P. T. Wang ²

¹ Mathematics Research Centre, Faculty of Information Technology and Communication Sciences, Tampere University, P.O. Box 692, 33101 Tampere, Finland
² Department of Mathematics, University College London, London, WC1H 0AY, United Kingdom

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Lassi Paunonen and Nicolas Vanspranghe and Ruoyu P. T. Wang},
     title = {Weakly elliptic damping gives sharp decay},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1263--1275},
     year = {2025},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     doi = {10.5802/crmath.767},
     language = {en},
}

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Lassi Paunonen; Nicolas Vanspranghe; Ruoyu P. T. Wang. Weakly elliptic damping gives sharp decay. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 1263-1275. doi: 10.5802/crmath.767

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