Decay rates for Kelvin-Voigt damped wave equations II: The geometric control condition
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- by Nicolas Burq and Chenmin Sun
- Proc. Amer. Math. Soc. 150 (2022), 1021-1039
- DOI: https://doi.org/10.1090/proc/15493
- Published electronically: December 22, 2021
Abstract:
We study in this article decay rates for Kelvin-Voigt damped wave equations under a geometric control condition. When the damping coefficient is sufficiently smooth ($C^1$ vanishing nicely, see the following equation: $|\nabla a|\leqslant Ca^{\frac {1}{2}}$) we show that exponential decay follows from geometric control conditions (see Nicolas Burq and Hans Christianson [Comm. Math. Phys. 336 (2015), pp. 101–130] and Louis Tebou [C. R. Math. Acad. Sci. Paris 350 (2012), pp. 603–608] for similar results under stronger assumptions on the damping function).References
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Bibliographic Information
- Nicolas Burq
- Affiliation: Université Paris-Saclay, Laboratoire de mathématiques d’Orsay, UMR 8628 du CNRS, Bâtiment 307, 91405 Orsay Cedex, France; and Institut Universitaire de France
- MR Author ID: 315457
- ORCID: 0000-0002-1121-3787
- Email: nicolas.burq@math.u-psud.fr
- Chenmin Sun
- Affiliation: Université de Cergy-Pontoise, Laboratoire de Mathématiques AGM, UMR 8088 du CNRS, 2 av. Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France
- MR Author ID: 1223962
- ORCID: 0000-0001-9481-3480
- Email: chenmin.sun@u-cergy.fr
- Received by editor(s): October 12, 2020
- Received by editor(s) in revised form: December 31, 2020
- Published electronically: December 22, 2021
- Additional Notes: The first author was supported by Institut Universitaire de France and ANR grant ISDEEC, ANR-16-CE40-0013. The second author was supported by the postdoc program: “Initiative d’Excellence Paris Seine” of CY Cergy-Paris Université and ANR grant ODA (ANR-18-CE40- 0020-01).
- Communicated by: Tanya Christiansen
- © Copyright 2021 by the authors
- Journal: Proc. Amer. Math. Soc. 150 (2022), 1021-1039
- MSC (2020): Primary 35L05, 58J47, 93D15
- DOI: https://doi.org/10.1090/proc/15493
- MathSciNet review: 4375701