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An identification problem for a linear evolution equation in a Banach space and applications
Exponential stability of the wave equation with boundary time-varying delay
1. | Université de Valenciennes et du Hainaut Cambrésis, LAMAV and FR CNRS 2956, Le Mont Houy, Institut des Sciences et Techniques de Valenciennes, 59313 Valenciennes Cedex 9 |
2. | Dipartimento di Matematica Pura e Applicata, Università di L'Aquila, Via Vetoio, Loc. Coppito, 67010 L'Aquila |
3. | Institut Elie Cartan de Nancy, Université Henri Poincaré, B.P. 70239, 54506 Vandoeuvre-lès-Nancy Cedex, France |
References:
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References:
[1] |
Serge Nicaise, Julie Valein. Stabilization of the wave equation on 1-d networks with a delay term in the nodal feedbacks. Networks and Heterogeneous Media, 2007, 2 (3) : 425-479. doi: 10.3934/nhm.2007.2.425 |
[2] |
Ferhat Mohamed, Hakem Ali. Energy decay of solutions for the wave equation with a time-varying delay term in the weakly nonlinear internal feedbacks. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 491-506. doi: 10.3934/dcdsb.2017024 |
[3] |
Yanni Guo, Genqi Xu, Yansha Guo. Stabilization of the wave equation with interior input delay and mixed Neumann-Dirichlet boundary. Discrete and Continuous Dynamical Systems - B, 2016, 21 (8) : 2491-2507. doi: 10.3934/dcdsb.2016057 |
[4] |
Kim Dang Phung. Boundary stabilization for the wave equation in a bounded cylindrical domain. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 1057-1093. doi: 10.3934/dcds.2008.20.1057 |
[5] |
Behzad Azmi, Karl Kunisch. Receding horizon control for the stabilization of the wave equation. Discrete and Continuous Dynamical Systems, 2018, 38 (2) : 449-484. doi: 10.3934/dcds.2018021 |
[6] |
Serge Nicaise. Internal stabilization of a Mindlin-Timoshenko model by interior feedbacks. Mathematical Control and Related Fields, 2011, 1 (3) : 331-352. doi: 10.3934/mcrf.2011.1.331 |
[7] |
Bei Gong, Zhen-Hu Ning, Fengyan Yang. Stabilization of the transmission wave/plate equation with variable coefficients on $ {\mathbb{R}}^n $. Evolution Equations and Control Theory, 2021, 10 (2) : 321-331. doi: 10.3934/eect.2020068 |
[8] |
Xiaorui Wang, Genqi Xu. Uniform stabilization of a wave equation with partial Dirichlet delayed control. Evolution Equations and Control Theory, 2020, 9 (2) : 509-533. doi: 10.3934/eect.2020022 |
[9] |
Zhiling Guo, Shugen Chai. Exponential stabilization of the problem of transmission of wave equation with linear dynamical feedback control. Evolution Equations and Control Theory, 2022 doi: 10.3934/eect.2022001 |
[10] |
Mokhtar Kirane, Belkacem Said-Houari, Mohamed Naim Anwar. Stability result for the Timoshenko system with a time-varying delay term in the internal feedbacks. Communications on Pure and Applied Analysis, 2011, 10 (2) : 667-686. doi: 10.3934/cpaa.2011.10.667 |
[11] |
Martin Gugat, Günter Leugering, Ke Wang. Neumann boundary feedback stabilization for a nonlinear wave equation: A strict $H^2$-lyapunov function. Mathematical Control and Related Fields, 2017, 7 (3) : 419-448. doi: 10.3934/mcrf.2017015 |
[12] |
Mohammad Akil, Ali Wehbe. Stabilization of multidimensional wave equation with locally boundary fractional dissipation law under geometric conditions. Mathematical Control and Related Fields, 2019, 9 (1) : 97-116. doi: 10.3934/mcrf.2019005 |
[13] |
Mokhtari Yacine. Boundary controllability and boundary time-varying feedback stabilization of the 1D wave equation in non-cylindrical domains. Evolution Equations and Control Theory, 2022, 11 (2) : 373-397. doi: 10.3934/eect.2021004 |
[14] |
Imene Aicha Djebour, Takéo Takahashi, Julie Valein. Feedback stabilization of parabolic systems with input delay. Mathematical Control and Related Fields, 2022, 12 (2) : 405-420. doi: 10.3934/mcrf.2021027 |
[15] |
Serge Nicaise, Cristina Pignotti. Stability of the wave equation with localized Kelvin-Voigt damping and boundary delay feedback. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 791-813. doi: 10.3934/dcdss.2016029 |
[16] |
Yaru Xie, Genqi Xu. Exponential stability of 1-d wave equation with the boundary time delay based on the interior control. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 557-579. doi: 10.3934/dcdss.2017028 |
[17] |
Guo Lin, Haiyan Wang. Traveling wave solutions of a reaction-diffusion equation with state-dependent delay. Communications on Pure and Applied Analysis, 2016, 15 (2) : 319-334. doi: 10.3934/cpaa.2016.15.319 |
[18] |
Vanessa Barros, Carlos Nonato, Carlos Raposo. Global existence and energy decay of solutions for a wave equation with non-constant delay and nonlinear weights. Electronic Research Archive, 2020, 28 (1) : 205-220. doi: 10.3934/era.2020014 |
[19] |
Alberto Bressan, Fabio S. Priuli. Nearly optimal patchy feedbacks. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 687-701. doi: 10.3934/dcds.2008.21.687 |
[20] |
Andrei Fursikov. Stabilization of the simplest normal parabolic equation. Communications on Pure and Applied Analysis, 2014, 13 (5) : 1815-1854. doi: 10.3934/cpaa.2014.13.1815 |
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