Open Access
Issue |
ESAIM: COCV
Volume 31, 2025
|
|
---|---|---|
Article Number | 43 | |
Number of page(s) | 29 | |
DOI | https://doi.org/10.1051/cocv/2025031 | |
Published online | 14 May 2025 |
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York (1983). [CrossRef] [Google Scholar]
- C. Bardos, G. Lebeau and J. Rauch, Un exemple d’utilisation des notions de propagation pour le contrôle et la stabilisation de problèmes hyperboliques. Rend. Sem. Mat. Univ. Politec. Torino (Special Issue) 11–31 (1989) 1988. [Google Scholar]
- C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J. Control Optim. 30 (1992) 1024–1065. [Google Scholar]
- J. Rauch and M. Taylor, Exponential decay of solutions to hyperbolic equations in bounded domains. Indiana Univ. Math. J. 24 (1974) 79–86. [CrossRef] [MathSciNet] [Google Scholar]
- N. Burq and R. Joly, Exponential decay for the damped wave equation in unbounded domains. Commun. Contemp. Math. 18 (2016) 1650012. [CrossRef] [MathSciNet] [Google Scholar]
- R.P.T. Wang, Exponential decay for damped Klein–Gordon equations on asymptotically cylindrical and conic manifolds. Ann. Inst. Fourier 74 (2024) 2623–2666. [CrossRef] [MathSciNet] [Google Scholar]
- J.-M. Bouclet and J. Royer, Local energy decay for the damped wave equation. J. Funct. Anal. 266 (2014) 4538–4615. [CrossRef] [MathSciNet] [Google Scholar]
- J. Royer, Local decay for the damped wave equation in the energy space. J. Inst. Math. Jussieu 17 (2018) 509–540. [CrossRef] [MathSciNet] [Google Scholar]
- J. Wunsch, Periodic damping gives polynomial energy decay. Math. Res. Lett. 24 (2017) 571–580. [CrossRef] [MathSciNet] [Google Scholar]
- R. Joly and J. Royer, Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation. J. Math. Soc. Japan 70 (2018) 1375–1418. [CrossRef] [MathSciNet] [Google Scholar]
- J. Royer, Energy decay for the Klein–Gordon equation with highly oscillating damping. Ann. H. Lebesgue 1 (2018) 297–312. [Google Scholar]
- K.-J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations. Vol. 194 of Graduate Texts in Mathematics. Springer-Verlag, New York (2000). [Google Scholar]
- N. Burq and P. Gèrard, Stabilization of wave equations on the torus with rough dampings. Pure Appl. Anal. 2 (2020) 627–658. [CrossRef] [MathSciNet] [Google Scholar]
- E. Zuazua, Exponential decay for the semilinear wave equation with localized damping in unbounded domains. J. Math. Pures Appl. 70 (1991) 513–529. [MathSciNet] [Google Scholar]
- L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. III. Springer-Verlag (1985). Second printing 1994. [Google Scholar]
- N. Lerner, Metrics on the Phase Space and Non-selfadjoint Pseudo-differential operators. Birkhäuser Verlag, Basel (2010). [CrossRef] [Google Scholar]
- M. Zworski, Semiclassical analysis. Vol. 138 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2012). [Google Scholar]
- G. Lebeau, Èquation des ondes amorties, in Algebraic and geometric methods in mathematical physics (Kaciveli, 1993), Vol. 19 of Math. Phys. Stud. Kluwer Acad. Publ., Dordrecht (1996) 73–109. [Google Scholar]
- M.E. Taylor, Partial differential equations 2: qualitative studies of linear equations. Vol. 116 of Applied Mathematical Sciences. Springer-Verlag, New York (1996). [Google Scholar]
- M. Lèautaud, Long time energy averages and a lower resolvent estimate for damped waves. arXiv:2309.12709 [math.AP] (2023). [Google Scholar]
- A. Prouff, Observability of the Schrödinger equation with subquadratic confining potential in the Euclidean space. arXiv:2307.00839 [math.AP] (2023). Accepted in Analysis & PDE. [Google Scholar]
- M. Dimassi and J. Sjöstrand, Spectral asymptotics in the semi-classical limit. Vol. 268 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (1999). [Google Scholar]
- P. Gèrard, Microlocal defect measures. Commun. Part. Differ. Equ. 16 (1991) 1761–1794. [CrossRef] [Google Scholar]
- P.-L. Lions and T. Paul, Sur les mesures de Wigner. Rev. Mat. Iberoamericana 9 (1993) 553–618. [CrossRef] [MathSciNet] [Google Scholar]
- N. Anantharaman and M. Lèautaud, Sharp polynomial decay rates for the damped wave equation on the torus. Anal. PDE 7 (2014) 159–214. [CrossRef] [MathSciNet] [Google Scholar]
- L. Gearhart, Spectral theory for contraction semigroups on Hilbert space. Trans. Amer. Math. Soc. 236 (1978) 385–394. [CrossRef] [MathSciNet] [Google Scholar]
- F.L. Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces. Ann. Differ. Equ. 1 (1985) 43–56. [Google Scholar]
- J. Prüss, On the spectrum of C0-semigroups. Trans. Amer. Math. Soc. 284 (1984) 847–857. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.