A ONE-DIMENSIONAL WAVE EQUATION WITH NONLINEAR DAMPING

STEFANIA GATTI; VITTORINO PATA

doi:10.1017/S0017089506003156

Abstract

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We consider a one-dimensional weakly damped wave equation, with a damping coefficient depending on the displacement. We prove the existence of a regular connected global attractor of finite fractal dimension for the associated dynamical system, as well as the existence of an exponential attractor.

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Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Kolbasin, Stanislav 2009. Attractors for Kirchhoff’s equation with a nonlinear damping coefficient. Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, Issue. 5-6, p. 2361.

Khanmamedov, A.Kh. 2010. A strong global attractor for the 3D wave equation with displacement dependent damping. Applied Mathematics Letters, Vol. 23, Issue. 8, p. 928.

Chueshov, Igor and Kolbasin, Stanislav 2010. Plate models with state-dependent damping coefficient and their quasi-static limits. Nonlinear Analysis: Theory, Methods & Applications, Vol. 73, Issue. 6, p. 1626.

Khanmamedov, A. Kh. 2010. Global attractors for 2-D wave equations with displacement-dependent damping. Mathematical Methods in the Applied Sciences, Vol. 33, Issue. 2, p. 177.

Khanmamedov, A.Kh. 2011. A global attractor for the plate equation with displacement-dependent damping. Nonlinear Analysis: Theory, Methods & Applications, Vol. 74, Issue. 5, p. 1607.

Khanmamedov, A.Kh. 2012. Global attractor for the one dimensional wave equation with displacement dependent damping. Applied Mathematics Letters, Vol. 25, Issue. 3, p. 439.

Chueshov, Igor and Kolbasin, Stanislav 2012. Long-time dynamics in plate models with strong nonlinear damping. Communications on Pure & Applied Analysis, Vol. 11, Issue. 2, p. 659.

Chueshov, Igor 2012. Long-time dynamics of Kirchhoff wave models with strong nonlinear damping. Journal of Differential Equations, Vol. 252, Issue. 2, p. 1229.

Colucci, Renato and Chacón, Gerardo R. 2013. Hyperbolic Relaxation of a Fourth Order Evolution Equation. Abstract and Applied Analysis, Vol. 2013, Issue. , p. 1.

Meng, Fengjuan and Zhong, Chengkui 2014. Multiple equilibrium points in global attractor for the weakly damped wave equation with critical exponent. Discrete & Continuous Dynamical Systems - B, Vol. 19, Issue. 1, p. 217.

V. Chepyzhov, Vladimir Conti, Monica and Pata, Vittorino 2014. Totally dissipative dynamical processes and their uniform global attractors. Communications on Pure & Applied Analysis, Vol. 13, Issue. 5, p. 1989.

Chueshov, Igor 2015. Dynamics of Quasi-Stable Dissipative Systems. p. 1.

Conti, Monica and Pata, Vittorino 2015. On the time-dependent Cattaneo law in space dimension one. Applied Mathematics and Computation, Vol. 259, Issue. , p. 32.

Chueshov, Igor 2015. Dynamics of Quasi-Stable Dissipative Systems. p. 285.

Chueshov, Igor 2015. Dynamics of Quasi-Stable Dissipative Systems. p. 219.

Egger, H Kugler, T and Strogies, N 2017. Parameter identification in a semilinear hyperbolic system. Inverse Problems, Vol. 33, Issue. 5, p. 055022.

Egger, Herbert and Kugler, Thomas 2018. Theory, Numerics and Applications of Hyperbolic Problems I. Vol. 236, Issue. , p. 515.

Egger, H. and Kugler, T. 2018. Damped wave systems on networks: exponential stability and uniform approximations. Numerische Mathematik, Vol. 138, Issue. 4, p. 839.

Ma, Qiaozhen and Wang, Lulu 2025. Uniform attractors of non-autonomous wave equations with singularly oscillating external forces and displacement-dependent damping. Journal of Differential Equations, Vol. 426, Issue. , p. 388.

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A ONE-DIMENSIONAL WAVE EQUATION WITH NONLINEAR DAMPING

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

A ONE-DIMENSIONAL WAVE EQUATION WITH NONLINEAR DAMPING

Abstract

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