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Decay of solutions to generalized plate type equations with memory
1. | School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China, China |
References:
[1] |
M. E. Bradley and S. Lenhart, Bilinear spatial control of the velocity term in a Kirchhoff plate equation, Electron. J. Differential Equations, 2001, 15 pp. |
[2] |
C. Buriol, Energy decay rates for the Timoshenko system of thermoelastic plates, Nonlinear Analysis, 64 (2006), 92-108.
doi: 10.1016/j.na.2005.06.010. |
[3] |
R. C. Charão, E. Bisognin, V. Bisognin and A. F. Pazoto, Asymptotic behavior for a dissipative plate equation in $\mathbb{R}^N2$ with periodic coefficients, Electron. J. Differential Equations, 2008, 23 pp. |
[4] |
C. R. da Luz and R. C. Charão, Asymptotic properties for a semilinear plate equation in unbounded domains, J. Hyperbolic Differ. Equ., 6 (2009), 269-294.
doi: 10.1142/S0219891609001824. |
[5] |
P. M. N. Dharmawardane, J. E. Muñoz Rivera and S. Kawashima, Decay property for second order hyperbolic systems of viscoelastic materials, J. Math. Anal. Appl., 366 (2010), 621-635.
doi: 10.1016/j.jmaa.2009.12.019. |
[6] |
Y. Enomoto, On a thermoelastic plate equation in an exterior domain, Math. Meth. Appl. Sci., 25 (2002), 443-472.
doi: 10.1002/mma.290. |
[7] |
T. Hosono and S. Kawashima, Decay property of regularity-loss type and application to some nonlinear hyperbolic-elliptic system, Math. Models Meth. Appl. Sci., 16 (2006), 1839-1859.
doi: 10.1142/S021820250600173X. |
[8] |
K. Ide and S. Kawashima, Decay property of regularity-loss type and nonlinear effects for dissipative Timoshenko system, Math. Models Meth. Appl. Sci., 18 (2008), 1001-1025.
doi: 10.1142/S0218202508002930. |
[9] |
H. J. Lee, Uniform decay for solution of the plate equation with a boundary condition of memory type, Trends in Math., 9 (2006), 51-55. |
[10] |
Y. Liu, Decay of solutions to an inertial model for a semilinear plate equation with memory, J. Math. Anal. Appl., 394 (2012), 616-632.
doi: 10.1016/j.jmaa.2012.04.003. |
[11] |
Y. Liu and S. Kawashima, Global existence and asymptotic behavior of solutions for quasi-linear dissipative plate equation, Discrete Contin. Dyn. Syst., 29 (2011), 1113-1139. |
[12] |
Y. Liu and S. Kawashima, Global existence and decay of solutions for a quasi-linear dissipative plate equation, J. Hyperbolic Diff. Equ., 8 (2011), 591-614.
doi: 10.1142/S0219891611002500. |
[13] |
Y. Liu and S. Kawashima, Decay property for a plate equation with memory-type dissipation, Kinet. Relat. Mod., 4 (2011), 531-547.
doi: 10.3934/krm.2011.4.531. |
[14] |
J. E. Muñoz Rivera, M. G. Naso and F. M. Vegni, Asymptotic behavior of the energy for a class of weakly dissipative second-order systems with memory, J. Math. Anal. Appl., 286 (2003), 692-704.
doi: 10.1016/S0022-247X(03)00511-0. |
[15] |
Y. Sugitani and S. Kawashima, Decay estimates of solutions to a semi-linear dissipative plate equation, J. Hyperbolic Differ. Equ., 7 (2010), 471-501.
doi: 10.1142/S0219891610002207. |
show all references
References:
[1] |
M. E. Bradley and S. Lenhart, Bilinear spatial control of the velocity term in a Kirchhoff plate equation, Electron. J. Differential Equations, 2001, 15 pp. |
[2] |
C. Buriol, Energy decay rates for the Timoshenko system of thermoelastic plates, Nonlinear Analysis, 64 (2006), 92-108.
doi: 10.1016/j.na.2005.06.010. |
[3] |
R. C. Charão, E. Bisognin, V. Bisognin and A. F. Pazoto, Asymptotic behavior for a dissipative plate equation in $\mathbb{R}^N2$ with periodic coefficients, Electron. J. Differential Equations, 2008, 23 pp. |
[4] |
C. R. da Luz and R. C. Charão, Asymptotic properties for a semilinear plate equation in unbounded domains, J. Hyperbolic Differ. Equ., 6 (2009), 269-294.
doi: 10.1142/S0219891609001824. |
[5] |
P. M. N. Dharmawardane, J. E. Muñoz Rivera and S. Kawashima, Decay property for second order hyperbolic systems of viscoelastic materials, J. Math. Anal. Appl., 366 (2010), 621-635.
doi: 10.1016/j.jmaa.2009.12.019. |
[6] |
Y. Enomoto, On a thermoelastic plate equation in an exterior domain, Math. Meth. Appl. Sci., 25 (2002), 443-472.
doi: 10.1002/mma.290. |
[7] |
T. Hosono and S. Kawashima, Decay property of regularity-loss type and application to some nonlinear hyperbolic-elliptic system, Math. Models Meth. Appl. Sci., 16 (2006), 1839-1859.
doi: 10.1142/S021820250600173X. |
[8] |
K. Ide and S. Kawashima, Decay property of regularity-loss type and nonlinear effects for dissipative Timoshenko system, Math. Models Meth. Appl. Sci., 18 (2008), 1001-1025.
doi: 10.1142/S0218202508002930. |
[9] |
H. J. Lee, Uniform decay for solution of the plate equation with a boundary condition of memory type, Trends in Math., 9 (2006), 51-55. |
[10] |
Y. Liu, Decay of solutions to an inertial model for a semilinear plate equation with memory, J. Math. Anal. Appl., 394 (2012), 616-632.
doi: 10.1016/j.jmaa.2012.04.003. |
[11] |
Y. Liu and S. Kawashima, Global existence and asymptotic behavior of solutions for quasi-linear dissipative plate equation, Discrete Contin. Dyn. Syst., 29 (2011), 1113-1139. |
[12] |
Y. Liu and S. Kawashima, Global existence and decay of solutions for a quasi-linear dissipative plate equation, J. Hyperbolic Diff. Equ., 8 (2011), 591-614.
doi: 10.1142/S0219891611002500. |
[13] |
Y. Liu and S. Kawashima, Decay property for a plate equation with memory-type dissipation, Kinet. Relat. Mod., 4 (2011), 531-547.
doi: 10.3934/krm.2011.4.531. |
[14] |
J. E. Muñoz Rivera, M. G. Naso and F. M. Vegni, Asymptotic behavior of the energy for a class of weakly dissipative second-order systems with memory, J. Math. Anal. Appl., 286 (2003), 692-704.
doi: 10.1016/S0022-247X(03)00511-0. |
[15] |
Y. Sugitani and S. Kawashima, Decay estimates of solutions to a semi-linear dissipative plate equation, J. Hyperbolic Differ. Equ., 7 (2010), 471-501.
doi: 10.1142/S0219891610002207. |
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