-
Previous Article
Estimating thermal insulating ability of anisotropic coatings via Robin eigenvalues and eigenfunctions
- DCDS Home
- This Issue
-
Next Article
Index sums of isolated singular points of positive vector fields
Global and exponential attractors for the singularly perturbed extensible beam
| 1. | Politecnico di Milano - Dipartimento di Matematica "F.Brioschi", Via Bonardi 9, 20133 Milano, Italy |
ε∂ttu + $\delta$∂tu+ $\omega$∂xxxx u-$[\beta+\int_0^1[\partial_y u(y,t)]^2\d y ]$∂xxu=f,
which describes the motion of the vertical deflection of an extensible Kirchhoff beam. The existence of the global attractor of optimal regularity is shown, as well as the existence of a family of exponential attractors Hölder-continuous in the symmetric Hausdorff distance (with respect to ε) and of finite fractal dimension uniformly bounded with respect to ε.
| [1] |
Takayuki Niimura. Attractors and their stability with respect to rotational inertia for nonlocal extensible beam equations. Discrete and Continuous Dynamical Systems, 2020, 40 (5) : 2561-2591. doi: 10.3934/dcds.2020141 |
| [2] |
Yue Sun, Zhijian Yang. Strong attractors and their robustness for an extensible beam model with energy damping. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 3101-3129. doi: 10.3934/dcdsb.2021175 |
| [3] |
Chunxiang Zhao, Chunyan Zhao, Chengkui Zhong. The global attractor for a class of extensible beams with nonlocal weak damping. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 935-955. doi: 10.3934/dcdsb.2019197 |
| [4] |
Yanan Li, Zhijian Yang, Fang Da. Robust attractors for a perturbed non-autonomous extensible beam equation with nonlinear nonlocal damping. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 5975-6000. doi: 10.3934/dcds.2019261 |
| [5] |
Alessia Berti, Maria Grazia Naso. Vibrations of a damped extensible beam between two stops. Evolution Equations and Control Theory, 2013, 2 (1) : 35-54. doi: 10.3934/eect.2013.2.35 |
| [6] |
Marcio Antonio Jorge da Silva, Vando Narciso. Attractors and their properties for a class of nonlocal extensible beams. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 985-1008. doi: 10.3934/dcds.2015.35.985 |
| [7] |
Eduardo Henrique Gomes Tavares, Vando Narciso. Attractors for a class of extensible beams with strong nonlinear damping. Evolution Equations and Control Theory, 2022 doi: 10.3934/eect.2022013 |
| [8] |
Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Júnior, Mauro L. Santos. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2805-2828. doi: 10.3934/dcdsb.2020206 |
| [9] |
Alessia Berti, Valeria Berti, Ivana Bochicchio. Global and exponential attractors for a Ginzburg-Landau model of superfluidity. Discrete and Continuous Dynamical Systems - S, 2011, 4 (2) : 247-271. doi: 10.3934/dcdss.2011.4.247 |
| [10] |
Manil T. Mohan. Global attractors, exponential attractors and determining modes for the three dimensional Kelvin-Voigt fluids with "fading memory". Evolution Equations and Control Theory, 2022, 11 (1) : 125-167. doi: 10.3934/eect.2020105 |
| [11] |
José A. Langa, Alain Miranville, José Real. Pullback exponential attractors. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1329-1357. doi: 10.3934/dcds.2010.26.1329 |
| [12] |
Xiu-Fang Liu, Gen-Qi Xu. Exponential stabilization of Timoshenko beam with input and output delays. Mathematical Control and Related Fields, 2016, 6 (2) : 271-292. doi: 10.3934/mcrf.2016004 |
| [13] |
Lin Yang, Yejuan Wang, Tomás Caraballo. Regularity of global attractors and exponential attractors for $ 2 $D quasi-geostrophic equations with fractional dissipation. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1345-1377. doi: 10.3934/dcdsb.2021093 |
| [14] |
Manil T. Mohan. Global and exponential attractors for the 3D Kelvin-Voigt-Brinkman-Forchheimer equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3393-3436. doi: 10.3934/dcdsb.2020067 |
| [15] |
Etsushi Nakaguchi, Koichi Osaki. Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (10) : 2627-2646. doi: 10.3934/dcdsb.2013.18.2627 |
| [16] |
T. F. Ma, M. L. Pelicer. Attractors for weakly damped beam equations with $p$-Laplacian. Conference Publications, 2013, 2013 (special) : 525-534. doi: 10.3934/proc.2013.2013.525 |
| [17] |
Dalibor Pražák. Exponential attractor for the delayed logistic equation with a nonlinear diffusion. Conference Publications, 2003, 2003 (Special) : 717-726. doi: 10.3934/proc.2003.2003.717 |
| [18] |
Messoud Efendiev, Anna Zhigun. On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis. Discrete and Continuous Dynamical Systems, 2018, 38 (2) : 651-673. doi: 10.3934/dcds.2018028 |
| [19] |
Kei Matsuura, Mitsuharu Otani. Exponential attractors for a quasilinear parabolic equation. Conference Publications, 2007, 2007 (Special) : 713-720. doi: 10.3934/proc.2007.2007.713 |
| [20] |
Alexandre Rodrigues. "Large" strange attractors in the unfolding of a heteroclinic attractor. Discrete and Continuous Dynamical Systems, 2022, 42 (5) : 2355-2379. doi: 10.3934/dcds.2021193 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]