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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 8: PDE's, Semigroup Theory, Inverse and Control Problems
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Original Articles

Geometrically constrained stabilization of wave equations with Wentzell boundary conditions

Marcelo M. Cavalcanti Department of Mathematics, State University of Maringá, 87020-900 Maringá, PR, Brazil
,
Irena Lasiecka Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA, Department of Mathematics, KFUPM, Dhahran, KSA, Saudi ArabiaCorrespondence[email protected]
&
Daniel Toundykov Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, 68588, USA
Pages 1427-1452 | Received 10 Jun 2011, Accepted 30 Nov 2011, Published online: 17 Jan 2012

Citations (21)

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Lila Ihaddadene & Ammar Khemmoudj. (2022) General decay for a wave equation with Wentzell boundary conditions and nonlinear delay terms. International Journal of Control 95:9, pages 2565-2580.
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Mikhail Kamenskii, Ching-Feng Wen & Margarita Zvereva. (2020) On a variational problem for a model of a Stieltjes string with a backlash at the end. Optimization 69:9, pages 1935-1959.
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Ammar Khemmoudj & Mohammed Essalih Aries. (2019) Stabilisation of a wave equation with localised memory term and boundary frictional damping. International Journal of Control 92:10, pages 2383-2395.
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Articles from other publishers (18)

José G. Simion Antunes, Marcelo M. Cavalcanti & Valéria N. Domingos Cavalcanti. (2023) Uniform decay rate estimates for the 2D wave equation posed in an inhomogeneous medium with exponential growth source term, locally distributed nonlinear dissipation, and dynamic Cauchy–Ventcel–type boundary conditions. Mathematische Nachrichten 297:3, pages 962-997.
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Dounya Kechiche, Ammar Khemmoudj & Mohammed Medjden. (2023) Exponential stability result for the wave equation with Kelvin–Voigt damping and past history subject to Wentzell boundary condition and delay term. Mathematical Methods in the Applied Sciences 47:3, pages 1546-1576.
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Chan Li, Jin Liang & Ti-Jun Xiao. (2023) Regularity and stability of wave equations with variable coefficients and Wentzell type boundary conditions. Journal of Differential Equations 374, pages 548-592.
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Abdelhakim Dahmani & Ammar Khemmoudj. (2022) Stability of the wave equation with localized Kelvin–Voigt damping and dynamic Wentzell boundary conditions with delay. Mathematical Methods in the Applied Sciences 46:4, pages 3649-3673.
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Chan Li. (2021) Asymptotics for Wave Equations with Damping Only on the Dynamical Boundary. Applied Mathematics & Optimization 84:S2, pages 2011-2026.
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A. F. Almeida, M. M. Cavalcanti, V. H. Gonzalez Martinez & J. P. Zanchetta. (2019) Uniform stabilization for the semilinear wave equation in an inhomogeneous medium with locally distributed nonlinear damping and dynamic Cauchy–Ventcel type boundary conditions. Communications in Contemporary Mathematics 23:03, pages 1950072.
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Chan Li & Kun‐Peng Jin. (2020) Asymptotics for 2‐D wave equations with Wentzell boundary conditions in the square. Mathematical Methods in the Applied Sciences 44:1, pages 265-273.
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Chan Li, Jin Liang & Ti-Jun Xiao. (2021) Asymptotic behaviours of solutions for wave equations with damped Wentzell boundary conditions but no interior damping. Journal of Differential Equations 271, pages 76-106.
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K. Laoubi & D. Seba. (2020) Polynomial Decay Rate for Dissipative Wave Equations with Mixed Boundary Conditions. Acta Applicandae Mathematicae 169:1, pages 629-646.
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Enzo Vitillaro. (2018) On the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and supercritical sources. Journal of Differential Equations 265:10, pages 4873-4941.
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Chan Li, Jin Liang & Ti-Jun Xiao. (2018) Dynamical behaviors of solutions to nonlinear wave equations with vanishing local damping and Wentzell boundary conditions. Zeitschrift für angewandte Mathematik und Physik 69:4.
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Wellington José Corrêa & Türker Özsarı. (2018) Complex Ginzburg–Landau equations with dynamic boundary conditions. Nonlinear Analysis: Real World Applications 41, pages 607-641.
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Denis Mercier, Serge Nicaise, Mohamad Ali Sammoury & Ali Wehbe. (2018) Indirect stability of the wave equation with a dynamic boundary control. Mathematische Nachrichten 291:7, pages 1114-1146.
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Fengyan Yang, Pengfei Yao & Goong Chen. (2018) Boundary controllability of structural acoustic systems with variable coefficients and curved walls. Mathematics of Control, Signals, and Systems 30:1.
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Chan Li, Jin Liang & Ti-Jun Xiao. (2017) Boundary stabilization for wave equations with damping only on the nonlinear Wentzell boundary. Nonlinear Analysis 164, pages 155-175.
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Rémi Buffe. (2017) Stabilization of the wave equation with Ventcel boundary condition. Journal de Mathématiques Pures et Appliquées 108:2, pages 207-259.
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Marcelo M. Cavalcanti, Valéria N. Domingos Cavalcanti, Ryuichi Fukuoka & Daniel Toundykov. (2013) Unified Approach to Stabilization of Waves on Compact Surfaces by Simultaneous Interior and Boundary Feedbacks of Unrestricted Growth. Applied Mathematics & Optimization 69:1, pages 83-122.
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Marcelo Cavalcanti, Irena Lasiecka & Daniel Toundykov. (2012) Wave equation with damping affecting only a subset of static Wentzell boundary is uniformly stable. Transactions of the American Mathematical Society 364:11, pages 5693-5713.
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