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On regularity of stochastic convolutions of functional linear differential equations with memory
Existence of pullback attractors for the non-autonomous suspension bridge equation with time delay
School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China |
We investigate the long-time behavior of solutions for the suspension bridge equation when the forcing term containing some hereditary characteristic. Existence of pullback attractor is shown by using the contractive function methods.
References:
[1] |
T. Caraballo, G. Łukaszewicz and J. Real,
Pullback attractors for asymptotically compact non-autonomous dynamical systems, Nonlinear Anal, 64 (2006), 484-498.
doi: 10.1016/j.na.2005.03.111. |
[2] |
T. Caraballo, P. E. Kloeden and J. Real,
Pullback and forward attractors for a damped wave equation with delays, Stoch. Dyn, 4 (2004), 405-423.
doi: 10.1142/S0219493704001139. |
[3] |
J. García-Luengo, P. Marín-Rubio and J. Real,
Some new regularity results of pullback attractors for 2D Navier-Stokes equations with delays, Commun. Pure Appl. Anal, 14 (2015), 1603-1621.
doi: 10.3934/cpaa.2015.14.1603. |
[4] |
J. García-Luegngo and P. Marín-Rubio,
Reaction-diffusion equations with non-autonomous force in $H^{-1}$ and delays under measurability conditions on the driving delay term, J. Math. Anal. Appl, 417 (2014), 80-95.
doi: 10.1016/j.jmaa.2014.03.026. |
[5] |
A. Kh. Khanmamedov,
Global attractors for a non-autonomous von Karman equations with nonlinear interior dissipation, Math. Anal. Appl, 318 (2006), 92-101.
doi: 10.1016/j.jmaa.2005.05.031. |
[6] |
A. C. Lazer and P. J. McKenna,
Large-amplitude periodic oscillations in suspension bridge: Some new connections with nonlinear analysis, SIAM Rev, 32 (1990), 537-578.
doi: 10.1137/1032120. |
[7] |
Q. Z. Ma and C. K. Zhong,
Existence of strong solutions and global attractors for the coupled suspension bridge equations, J. Differential Equations, 246 (2009), 3755-3775.
doi: 10.1016/j.jde.2009.02.022. |
[8] |
Q. Z. Ma and C. K. Zhong,
Existence of global attractors for the coupled system of suspension bridge equations, J. Math. Anal. Appl, 308 (2005), 365-379.
doi: 10.1016/j.jmaa.2005.01.036. |
[9] |
Q. Z. Ma and C. K. Zhong,
Existence of global attractors for the suspension bridge equations, J. Sichuan University (Natural Science Bridge Edition), 43 (2006), 271-276.
|
[10] |
Q. Z. Ma, S. P. Wang and X. B. Chen,
Uniform compact attractors for the coupled suspension bridge equations, Appl. Math. Comput, 217 (2011), 6604-6615.
doi: 10.1016/j.amc.2011.01.045. |
[11] |
Q. Z. Ma and B. L. Wang,
Existence of pullback attractors for the coupled suspension bridge equation, Electronic. J. Differential Equations, 2011 (2011), 1-10.
|
[12] |
Q. Z. Ma and L. Xu,
Random attractors for the coupled suspension bridge equations with white noises, Appl. Math. Comput, 306 (2017), 38-48.
doi: 10.1016/j.amc.2017.02.019. |
[13] |
Q. Z. Ma and L. Xu,
Random attractors for the extensible suspension bridge equation with white noise, Comput. Appl. Math., 70 (2015), 2895-2903.
doi: 10.1016/j.camwa.2015.09.029. |
[14] |
P. J. McKenna and W. Walter,
Nonlinear oscillation in a suspension bridge, Arch. Ration. Mech. Appl. Sci, 98 (1987), 167-177.
doi: 10.1007/BF00251232. |
[15] |
J. Y. Park and J. R. Kang,
Pullback D-attractors for non-autonomous suspension bridge equations, Nonlinear Anal, 71 (2009), 4618-4623.
doi: 10.1016/j.na.2009.03.025. |
[16] |
S. H. Park,
Long-time behavior for suspension bridge equations with time delay, Z. Angew. Math. Phys., 69 (2018), 1-12.
doi: 10.1007/s00033-018-0934-9. |
[17] |
S. H. Park,
Long-time dynamics of a von Karman equation with time delay, Appl. Math. Lett., 75 (2018), 128-134.
doi: 10.1016/j.aml.2017.07.004. |
[18] |
C. Y. Sun and K. X. Zhu, Pullback attractors for nonclassical diffusion equations with delays, J. Math. Phys, 56 (2015), 092703, 20 pp. |
[19] |
R. Temam, Infinite Dimensional Dynamical Systems in Mechanics abd Physics, Springer-Verlag, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |
[20] |
C. K. Zhong, Q. Z. Ma and C. Y. Sun,
Existence of strong solutions and global attractors for the suspension bridge equations, Nonlinear Anal., 67 (2007), 442-454.
doi: 10.1016/j.na.2006.05.018. |
show all references
References:
[1] |
T. Caraballo, G. Łukaszewicz and J. Real,
Pullback attractors for asymptotically compact non-autonomous dynamical systems, Nonlinear Anal, 64 (2006), 484-498.
doi: 10.1016/j.na.2005.03.111. |
[2] |
T. Caraballo, P. E. Kloeden and J. Real,
Pullback and forward attractors for a damped wave equation with delays, Stoch. Dyn, 4 (2004), 405-423.
doi: 10.1142/S0219493704001139. |
[3] |
J. García-Luengo, P. Marín-Rubio and J. Real,
Some new regularity results of pullback attractors for 2D Navier-Stokes equations with delays, Commun. Pure Appl. Anal, 14 (2015), 1603-1621.
doi: 10.3934/cpaa.2015.14.1603. |
[4] |
J. García-Luegngo and P. Marín-Rubio,
Reaction-diffusion equations with non-autonomous force in $H^{-1}$ and delays under measurability conditions on the driving delay term, J. Math. Anal. Appl, 417 (2014), 80-95.
doi: 10.1016/j.jmaa.2014.03.026. |
[5] |
A. Kh. Khanmamedov,
Global attractors for a non-autonomous von Karman equations with nonlinear interior dissipation, Math. Anal. Appl, 318 (2006), 92-101.
doi: 10.1016/j.jmaa.2005.05.031. |
[6] |
A. C. Lazer and P. J. McKenna,
Large-amplitude periodic oscillations in suspension bridge: Some new connections with nonlinear analysis, SIAM Rev, 32 (1990), 537-578.
doi: 10.1137/1032120. |
[7] |
Q. Z. Ma and C. K. Zhong,
Existence of strong solutions and global attractors for the coupled suspension bridge equations, J. Differential Equations, 246 (2009), 3755-3775.
doi: 10.1016/j.jde.2009.02.022. |
[8] |
Q. Z. Ma and C. K. Zhong,
Existence of global attractors for the coupled system of suspension bridge equations, J. Math. Anal. Appl, 308 (2005), 365-379.
doi: 10.1016/j.jmaa.2005.01.036. |
[9] |
Q. Z. Ma and C. K. Zhong,
Existence of global attractors for the suspension bridge equations, J. Sichuan University (Natural Science Bridge Edition), 43 (2006), 271-276.
|
[10] |
Q. Z. Ma, S. P. Wang and X. B. Chen,
Uniform compact attractors for the coupled suspension bridge equations, Appl. Math. Comput, 217 (2011), 6604-6615.
doi: 10.1016/j.amc.2011.01.045. |
[11] |
Q. Z. Ma and B. L. Wang,
Existence of pullback attractors for the coupled suspension bridge equation, Electronic. J. Differential Equations, 2011 (2011), 1-10.
|
[12] |
Q. Z. Ma and L. Xu,
Random attractors for the coupled suspension bridge equations with white noises, Appl. Math. Comput, 306 (2017), 38-48.
doi: 10.1016/j.amc.2017.02.019. |
[13] |
Q. Z. Ma and L. Xu,
Random attractors for the extensible suspension bridge equation with white noise, Comput. Appl. Math., 70 (2015), 2895-2903.
doi: 10.1016/j.camwa.2015.09.029. |
[14] |
P. J. McKenna and W. Walter,
Nonlinear oscillation in a suspension bridge, Arch. Ration. Mech. Appl. Sci, 98 (1987), 167-177.
doi: 10.1007/BF00251232. |
[15] |
J. Y. Park and J. R. Kang,
Pullback D-attractors for non-autonomous suspension bridge equations, Nonlinear Anal, 71 (2009), 4618-4623.
doi: 10.1016/j.na.2009.03.025. |
[16] |
S. H. Park,
Long-time behavior for suspension bridge equations with time delay, Z. Angew. Math. Phys., 69 (2018), 1-12.
doi: 10.1007/s00033-018-0934-9. |
[17] |
S. H. Park,
Long-time dynamics of a von Karman equation with time delay, Appl. Math. Lett., 75 (2018), 128-134.
doi: 10.1016/j.aml.2017.07.004. |
[18] |
C. Y. Sun and K. X. Zhu, Pullback attractors for nonclassical diffusion equations with delays, J. Math. Phys, 56 (2015), 092703, 20 pp. |
[19] |
R. Temam, Infinite Dimensional Dynamical Systems in Mechanics abd Physics, Springer-Verlag, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |
[20] |
C. K. Zhong, Q. Z. Ma and C. Y. Sun,
Existence of strong solutions and global attractors for the suspension bridge equations, Nonlinear Anal., 67 (2007), 442-454.
doi: 10.1016/j.na.2006.05.018. |
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