-
Previous Article
Fastest synchronized network and synchrony on the Julia set of complex-valued coupled map lattices
- DCDS-B Home
- This Issue
-
Next Article
Global stability of a delayed viral infection model with nonlinear immune response and general incidence rate
Existence of the global attractor for the plate equation with nonlocal nonlinearity in $ \mathbb{R} ^{n}$
1. | Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe 06800, Ankara, Turkey |
References:
[1] |
Z. Arat, A. Khanmamedov and S. Simsek, Global attractors for the plate equation with nonlocal nonlinearity in unbounded domains, Dynamics of PDE, 11 (2014), 361-379.
doi: 10.4310/DPDE.2014.v11.n4.a4. |
[2] |
J. Ball, Global attractors for semilinear wave equations, Discr. Cont. Dyn. Sys., 10 (2004), 31-52.
doi: 10.3934/dcds.2004.10.31. |
[3] |
F. Bucci and I. Chueshov, Long-time dynamics of a coupled system of nonlinear wave and thermoelastic plate equations, Discrete Contin. Dyn. Syst., 22 (2008), 557-586.
doi: 10.3934/dcds.2008.22.557. |
[4] |
T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations, Oxford University Press, New York, 1998. |
[5] |
I. Chueshov and S. Kolbasin, Long-time dynamics in plate models with strong nonlinear damping, Commun. Pure Appl. Anal., 11 (2012), 659-674.
doi: 10.3934/cpaa.2012.11.659. |
[6] |
I. Chueshov and I. Lasiecka, Von Karman Evolution Equations, Springer, Berlin, 2010.
doi: 10.1007/978-0-387-87712-9. |
[7] |
E. Dowell, Aeroelasticity of Plates and Shells, Nordhoff, Leyden, 1975. |
[8] |
E. Dowell, A Modern Course in Aeroelasticity, Springer, 2015.
doi: 10.1007/978-3-319-09453-3. |
[9] |
A. Kh. Khanmamedov, Existence of a global attractor for the plate equation with a critical exponent in an unbounded domain, Applied Mathematics Letters, 18 (2005), 827-832.
doi: 10.1016/j.aml.2004.08.013. |
[10] |
A. Kh. Khanmamedov, Global attractors for the plate equation with a localized damping and a critical exponent in an unbounded domain, J. Differential Equations, 225 (2006), 528-548.
doi: 10.1016/j.jde.2005.12.001. |
[11] |
A. Kh. Khanmamedov, Global attractors for von Karman equations with nonlinear interior dissipation, J. Math. Anal. Appl., 318 (2006), 92-101.
doi: 10.1016/j.jmaa.2005.05.031. |
[12] |
A. Kh. Khanmamedov, Global attractors for 2-D wave equations with displacement dependent damping, Math. Methods Appl. Sci., 33 (2010), 177-187.
doi: 10.1002/mma.1161. |
[13] |
A. Kh. Khanmamedov, A global attractors for plate equation with displacement-dependent damping, Nonlinear Analysis, 74 (2011), 1607-1615.
doi: 10.1016/j.na.2010.10.031. |
[14] |
S. Kolbasin, Attractors for Kirchoff's equation with a nonlinear damping coefficient, Nonlinear Analysis, 71 (2009), 2361-2371.
doi: 10.1016/j.na.2009.01.187. |
[15] |
W. Krolikowski and O. Bang, {Solitons in nonlocal nonlnear media: Exact solutions, Physical Review E, 63 (2000), 016610. |
[16] |
T. F. Ma and V. Narciso, Global attractor for a model of extensible beam with nonlinear damping and source terms, Nonlinear Anal., 73 (2010), 3402-3412.
doi: 10.1016/j.na.2010.07.023. |
[17] |
T. F. Ma, V. Narciso and M. L. Pelicer, Long-time behavior of a model of extensible beams with nonlinear boundary dissipations, J. Math. Anal. Appl., 396 (2012), 694-703.
doi: 10.1016/j.jmaa.2012.07.004. |
[18] |
M. Potomkin, {On transmission problem for Berger plates on an elastic base, Journal of Mathematical Physics, Analysis, Geometry, 7 (2011), 96-102. |
[19] |
M. Potomkin, A nonlinear transmission problem for acompound plate with thermoelastic part, Math. Methods Appl. Sci., 35 (2012), 530-546.
doi: 10.1002/mma.1589. |
[20] |
J. Simon, Compact sets in the space $L_p(0,T;B)$, Annali Mat. Pura Appl., 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
[21] |
A. Snyder and J. Mitchell, Accessible Solitons, Science, 276 (1997), 1538-1541.
doi: 10.1126/science.276.5318.1538. |
[22] |
L. Yang, Uniform attractor for non-autonomous plate equation with a localized damping and a critical nonlinearity, J. Math. Anal. Appl., 338 (2008), 1243-1254.
doi: 10.1016/j.jmaa.2007.06.011. |
[23] |
G. Yue and C. Zhong, Global attractors for plate equations with critical exponent in locally uniform spaces, Nonlinear Analysis, 71 (2009), 4105-4114.
doi: 10.1016/j.na.2009.02.089. |
show all references
References:
[1] |
Z. Arat, A. Khanmamedov and S. Simsek, Global attractors for the plate equation with nonlocal nonlinearity in unbounded domains, Dynamics of PDE, 11 (2014), 361-379.
doi: 10.4310/DPDE.2014.v11.n4.a4. |
[2] |
J. Ball, Global attractors for semilinear wave equations, Discr. Cont. Dyn. Sys., 10 (2004), 31-52.
doi: 10.3934/dcds.2004.10.31. |
[3] |
F. Bucci and I. Chueshov, Long-time dynamics of a coupled system of nonlinear wave and thermoelastic plate equations, Discrete Contin. Dyn. Syst., 22 (2008), 557-586.
doi: 10.3934/dcds.2008.22.557. |
[4] |
T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations, Oxford University Press, New York, 1998. |
[5] |
I. Chueshov and S. Kolbasin, Long-time dynamics in plate models with strong nonlinear damping, Commun. Pure Appl. Anal., 11 (2012), 659-674.
doi: 10.3934/cpaa.2012.11.659. |
[6] |
I. Chueshov and I. Lasiecka, Von Karman Evolution Equations, Springer, Berlin, 2010.
doi: 10.1007/978-0-387-87712-9. |
[7] |
E. Dowell, Aeroelasticity of Plates and Shells, Nordhoff, Leyden, 1975. |
[8] |
E. Dowell, A Modern Course in Aeroelasticity, Springer, 2015.
doi: 10.1007/978-3-319-09453-3. |
[9] |
A. Kh. Khanmamedov, Existence of a global attractor for the plate equation with a critical exponent in an unbounded domain, Applied Mathematics Letters, 18 (2005), 827-832.
doi: 10.1016/j.aml.2004.08.013. |
[10] |
A. Kh. Khanmamedov, Global attractors for the plate equation with a localized damping and a critical exponent in an unbounded domain, J. Differential Equations, 225 (2006), 528-548.
doi: 10.1016/j.jde.2005.12.001. |
[11] |
A. Kh. Khanmamedov, Global attractors for von Karman equations with nonlinear interior dissipation, J. Math. Anal. Appl., 318 (2006), 92-101.
doi: 10.1016/j.jmaa.2005.05.031. |
[12] |
A. Kh. Khanmamedov, Global attractors for 2-D wave equations with displacement dependent damping, Math. Methods Appl. Sci., 33 (2010), 177-187.
doi: 10.1002/mma.1161. |
[13] |
A. Kh. Khanmamedov, A global attractors for plate equation with displacement-dependent damping, Nonlinear Analysis, 74 (2011), 1607-1615.
doi: 10.1016/j.na.2010.10.031. |
[14] |
S. Kolbasin, Attractors for Kirchoff's equation with a nonlinear damping coefficient, Nonlinear Analysis, 71 (2009), 2361-2371.
doi: 10.1016/j.na.2009.01.187. |
[15] |
W. Krolikowski and O. Bang, {Solitons in nonlocal nonlnear media: Exact solutions, Physical Review E, 63 (2000), 016610. |
[16] |
T. F. Ma and V. Narciso, Global attractor for a model of extensible beam with nonlinear damping and source terms, Nonlinear Anal., 73 (2010), 3402-3412.
doi: 10.1016/j.na.2010.07.023. |
[17] |
T. F. Ma, V. Narciso and M. L. Pelicer, Long-time behavior of a model of extensible beams with nonlinear boundary dissipations, J. Math. Anal. Appl., 396 (2012), 694-703.
doi: 10.1016/j.jmaa.2012.07.004. |
[18] |
M. Potomkin, {On transmission problem for Berger plates on an elastic base, Journal of Mathematical Physics, Analysis, Geometry, 7 (2011), 96-102. |
[19] |
M. Potomkin, A nonlinear transmission problem for acompound plate with thermoelastic part, Math. Methods Appl. Sci., 35 (2012), 530-546.
doi: 10.1002/mma.1589. |
[20] |
J. Simon, Compact sets in the space $L_p(0,T;B)$, Annali Mat. Pura Appl., 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
[21] |
A. Snyder and J. Mitchell, Accessible Solitons, Science, 276 (1997), 1538-1541.
doi: 10.1126/science.276.5318.1538. |
[22] |
L. Yang, Uniform attractor for non-autonomous plate equation with a localized damping and a critical nonlinearity, J. Math. Anal. Appl., 338 (2008), 1243-1254.
doi: 10.1016/j.jmaa.2007.06.011. |
[23] |
G. Yue and C. Zhong, Global attractors for plate equations with critical exponent in locally uniform spaces, Nonlinear Analysis, 71 (2009), 4105-4114.
doi: 10.1016/j.na.2009.02.089. |
[1] |
I. D. Chueshov, Iryna Ryzhkova. A global attractor for a fluid--plate interaction model. Communications on Pure and Applied Analysis, 2013, 12 (4) : 1635-1656. doi: 10.3934/cpaa.2013.12.1635 |
[2] |
Francesca Bucci, Igor Chueshov, Irena Lasiecka. Global attractor for a composite system of nonlinear wave and plate equations. Communications on Pure and Applied Analysis, 2007, 6 (1) : 113-140. doi: 10.3934/cpaa.2007.6.113 |
[3] |
Moncef Aouadi, Alain Miranville. Quasi-stability and global attractor in nonlinear thermoelastic diffusion plate with memory. Evolution Equations and Control Theory, 2015, 4 (3) : 241-263. doi: 10.3934/eect.2015.4.241 |
[4] |
Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5321-5335. doi: 10.3934/dcdsb.2020345 |
[5] |
Biyue Chen, Chunxiang Zhao, Chengkui Zhong. The global attractor for the wave equation with nonlocal strong damping. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6207-6228. doi: 10.3934/dcdsb.2021015 |
[6] |
Tingting Liu, Qiaozhen Ma, Ling Xu. Attractor of the Kirchhoff type plate equation with memory and nonlinear damping on the whole time-dependent space. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022046 |
[7] |
Milena Stanislavova. On the global attractor for the damped Benjamin-Bona-Mahony equation. Conference Publications, 2005, 2005 (Special) : 824-832. doi: 10.3934/proc.2005.2005.824 |
[8] |
Wided Kechiche. Regularity of the global attractor for a nonlinear Schrödinger equation with a point defect. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1233-1252. doi: 10.3934/cpaa.2017060 |
[9] |
Zhijian Yang, Zhiming Liu. Global attractor for a strongly damped wave equation with fully supercritical nonlinearities. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2181-2205. doi: 10.3934/dcds.2017094 |
[10] |
D. Hilhorst, L. A. Peletier, A. I. Rotariu, G. Sivashinsky. Global attractor and inertial sets for a nonlocal Kuramoto-Sivashinsky equation. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 557-580. doi: 10.3934/dcds.2004.10.557 |
[11] |
Tomás Caraballo, Marta Herrera-Cobos, Pedro Marín-Rubio. Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution. Discrete and Continuous Dynamical Systems - B, 2017, 22 (5) : 1801-1816. doi: 10.3934/dcdsb.2017107 |
[12] |
Brahim Alouini. Global attractor for a one dimensional weakly damped half-wave equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (8) : 2655-2670. doi: 10.3934/dcdss.2020410 |
[13] |
Wided Kechiche. Global attractor for a nonlinear Schrödinger equation with a nonlinearity concentrated in one point. Discrete and Continuous Dynamical Systems - S, 2021, 14 (8) : 3027-3042. doi: 10.3934/dcdss.2021031 |
[14] |
Yongqin Liu, Shuichi Kawashima. Global existence and asymptotic behavior of solutions for quasi-linear dissipative plate equation. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1113-1139. doi: 10.3934/dcds.2011.29.1113 |
[15] |
Nobu Kishimoto, Minjie Shan, Yoshio Tsutsumi. Global well-posedness and existence of the global attractor for the Kadomtsev-Petviashvili Ⅱ equation in the anisotropic Sobolev space. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 1283-1307. doi: 10.3934/dcds.2020078 |
[16] |
George Avalos, Pelin G. Geredeli, Justin T. Webster. Finite dimensional smooth attractor for the Berger plate with dissipation acting on a portion of the boundary. Communications on Pure and Applied Analysis, 2016, 15 (6) : 2301-2328. doi: 10.3934/cpaa.2016038 |
[17] |
Muhammad I. Mustafa. Viscoelastic plate equation with boundary feedback. Evolution Equations and Control Theory, 2017, 6 (2) : 261-276. doi: 10.3934/eect.2017014 |
[18] |
Nikos I. Karachalios, Nikos M. Stavrakakis. Estimates on the dimension of a global attractor for a semilinear dissipative wave equation on $\mathbb R^N$. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 939-951. doi: 10.3934/dcds.2002.8.939 |
[19] |
Brahim Alouini. Finite dimensional global attractor for a Bose-Einstein equation in a two dimensional unbounded domain. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1781-1801. doi: 10.3934/cpaa.2015.14.1781 |
[20] |
Zhiming Liu, Zhijian Yang. Global attractor of multi-valued operators with applications to a strongly damped nonlinear wave equation without uniqueness. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 223-240. doi: 10.3934/dcdsb.2019179 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]