[1]
|
Arnold, L. (1998) Random Dynamical Systems. Springer-Verlag, New York and Berlin. http://dx.doi.org/10.1007/978-3-662-12878-7
|
[2]
|
Belleri, V. and Pata, V. (2001) Attractors for Semilinear Strongly Damped Wave Equations on . Discrete and Continuous Dynamical Systems, 7, 719-735. http://dx.doi.org/10.3934/dcds.2001.7.719
|
[3]
|
Conti, M., Pata, V. and Squassina, M. (2005) Strongly Damped Wave Equations on with Critical Nonlinearities. Communications on Pure and Applied Analysis, 9, 161-176.
|
[4]
|
Chen, F., Guo, B. and Wang, P. (1998) Long Time Behavior of Strongly Damped Nonlinear Wave Equations. Journal of Differential Equations, 147, 339-352. http://dx.doi.org/10.1006/jdeq.1998.3447
|
[5]
|
Li, H. and Zhou, S. (2008) On Non-Autonomous Strongly Damped Wave Equations with a Uniform Attractor and Some Averaging. Journal of Mathematical Analysis and Applications, 341, 791-802. http://dx.doi.org/10.1016/j.jmaa.2007.10.051
|
[6]
|
Temam, R. (1998) Infinite Dimensional Dynamical Systems in Mechanics and Physics. Springer-Verlag, New York.
|
[7]
|
Yang, M. and Sun, C. (2009) Attractors for Strongly Damped Wave Equations. Nonlinear Analysis: Real World Applications, 10, 1097-1100. http://dx.doi.org/10.1016/j.nonrwa.2007.12.001
|
[8]
|
Yang, M. and Sun, C. (2010) Exponential Attractors for the Strongly Damped Wave Equations. Nonlinear Analysis: Real World Applications, 11, 913-919. http://dx.doi.org/10.1016/j.nonrwa.2009.01.022
|
[9]
|
Zhou, S. (1999) Dimension of the Global Attractor for Strongly Damped Nonlinear Wave Equation. Journal of Mathematical Analysis and Applications, 233, 102-115. http://dx.doi.org/10.1006/jmaa.1999.6269
|
[10]
|
Zhou, S. and Fan, X. (2002) Kernel Sections for Non-Autonomous Strongly Damped Wave Equations. Journal of Mathematical Analysis and Applications, 275, 850-869. http://dx.doi.org/10.1016/S0022-247X(02)00437-7
|
[11]
|
Zhou, S. (2003) Attractors for Strongly Damped Wave Equations with Critical Exponent. Applied Mathematics Letters, 16, 1307-1314. http://dx.doi.org/10.1016/S0893-9659(03)90134-0
|
[12]
|
Chow, P. (2002) Stochastic Wave Equation with Polynomial Nonlinearity. Annals of Applied Probability, 12, 361-381. http://dx.doi.org/10.1214/aoap/1015961168
|
[13]
|
Fan, X. (2004) Random Attractor for a Damped Sine-Gordon Equation with White Noise. Pacific Journal of Mathematics, 216, 63-76. http://dx.doi.org/10.2140/pjm.2004.216.63
|
[14]
|
Fan, X. and Wang, Y. (2007) Fractal Dimensional of Attractors for a Stochastic Wave Equation with Nonlinear Damping and White Noise. Stochastic Analysis and Applications, 25, 381-396. http://dx.doi.org/10.1080/07362990601139602
|
[15]
|
Fan, X. (2008) Random Attractors for Damped Stochastic Wave Equations with Multiplicative Noise. International Journal of Mathematics, 19, 421-437. http://dx.doi.org/10.1142/S0129167X08004741
|
[16]
|
Fan, X. (2006) Attractors for a Damped Stochastic Wave Equation of Sine-Gordon Type with Sublinear Multiplicative Noise. Stochastic Analysis and Applications, 24, 767-793. http://dx.doi.org/10.1080/07362990600751860
|
[17]
|
Jones, R. and Wang, B. (2013) Asymptotic Behavior of a Class of Stochastic Nonlinear Wave Equations with Dispersive and Dissipative Terms. Nonlinear Analysis: Real World Applications, 14, 1308-1322. http://dx.doi.org/10.1016/j.nonrwa.2012.09.019
|
[18]
|
Lu, K. and Schmalfuß, B. (2007) Invariant Manifolds for Stochastic Wave Equations. Journal of Differential Equations, 236, 460-492. http://dx.doi.org/10.1016/j.jde.2006.09.024
|
[19]
|
Lv, Y. and Wang, W. (2008) Limiting Dynamics for Stochastic Wave Equations. Journal of Differential Equations, 244, 1-23. http://dx.doi.org/10.1016/j.jde.2007.10.009
|
[20]
|
Wang, B.X. and Gao, X.L. (2009) Random Attractors for Wave Equations on Unbounded Domains. Discrete and Continuous Dynamical Systems, Special, 800-809.
|
[21]
|
Wang, B. (2011) Asymptotic Behavior of Stochastic Wave Equations with Critical Exponents on . Transactions of the American Mathematical Society, 363, 3639-3663. http://dx.doi.org/10.1090/S0002-9947-2011-05247-5
|
[22]
|
Wang, Z., Zhou, S. and Gu, A. (2012) Random Attractor of the Stochastic Strongly Damped Wave Equation. Communications in Nonlinear Science and Numerical Simulation, 17, 1649-1658. http://dx.doi.org/10.1016/j.cnsns.2011.09.001
|
[23]
|
Wang, Z., Zhou, S. and Gu, A. (2011) Random Attractor for a Stochastic Damped Wave Equation with Multiplicative Noise on Unbounded Domains. Nonlinear Analysis: Real World Applications, 12, 3468-3482. http://dx.doi.org/10.1016/j.nonrwa.2011.06.008
|
[24]
|
Yang, M., Duan, J. and Kloeden, P. (2011) Asymptotic Behavior of Solutions for Random Wave Equations with Nonlinear Damping and White Noise. Nonlinear Analysis: Real World Applications, 12, 464-478. http://dx.doi.org/10.1016/j.nonrwa.2010.06.032
|
[25]
|
Zhou, S., Yin, F. and Ou Yang, Z. (2005) Random Attractor for Damped Nonlinear Wave Equations with White Noise. The SIAM Journal on Applied Dynamical Systems, 4, 883-903. http://dx.doi.org/10.1137/050623097
|
[26]
|
Crauel, H. (2002) Random Probability Measure on Polish Spaces. Taylor & Francis, London.
|
[27]
|
Crauel, H., Debussche, A. and Flandoli, F. (1997) Random Attractors. Journal of Dynamics and Differential Equations, 9, 307-341. http://dx.doi.org/10.1007/BF02219225
|
[28]
|
Crauel, H. and Flandoli, F. (1994) Attractors for Random Dynamical Systems. Probability Theory and Related Fields, 100, 365-393. http://dx.doi.org/10.1007/BF01193705
|
[29]
|
Flandoli, F. and Schmalfuß, B. (1996) Random Attractors for the 3D Stochastic Navier-Stokes Equation with Multiplicative Noise. Stochastics and Stochastic Reports, 59, 21-45. http://dx.doi.org/10.1080/17442509608834083
|
[30]
|
Shen, Z., Zhou, S. and Shen, W. (2010) One-Dimensional Random Attractor and Rotation Number of the Stochastic Damped Sine-Gordon Equation. Journal of Differential Equations, 248, 1432-1457. http://dx.doi.org/10.1016/j.jde.2009.10.007
|
[31]
|
Ball, J.M. (1997) Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations. Journal of Nonlinear Science, 7, 475-502. http://dx.doi.org/10.1007/s003329900037
|
[32]
|
Ball, J.M. (2004) Global Attractors for Damped Semilinear Wave Equations. Discrete and Continuous Dynamical Systems, 10, 31-52. http://dx.doi.org/10.3934/dcds.2004.10.31
|
[33]
|
Ghidaglia, J.M. (1994) A Note on the Strong Convergence towards Attractors for Damped Forced KdV Equations. Journal of Differential Equations, 110, 356-359. http://dx.doi.org/10.1006/jdeq.1994.1071
|
[34]
|
Goubet, O. and Rosa, R. (2002) Asymptotic Smoothing and the Global Attractor of a Weakly Damped KdV Equation on the Real Line. Journal of Differential Equations, 185, 25-53. http://dx.doi.org/10.1006/jdeq.2001.4163
|
[35]
|
Ju, N. (2000) The H1-Compact Global Attractor for the Solutions to the Navier-Stokes Equations in Two-Dimensional Unbounded Domains. Nonlinearity, 13, 1227-1238. http://dx.doi.org/10.1088/0951-7715/13/4/313
|
[36]
|
Moise, I. and Rosa, R. (1997) On the Regularity of the Global Attractor of a Weakly Damped, Forced Korteweg-de Vries Equation. Advances in Differential Equations, 2, 257-296.
|
[37]
|
Moise, I., Rosa, R. and Wang, X. (1998) Attractors for Non-Compact Semigroups via Energy Equations. Nonlinearity, 11, 1369-1393. http://dx.doi.org/10.1088/0951-7715/11/5/012
|
[38]
|
Rosa, R. (1998) The Global Attractor for the 2D Navier-Stokes Flow on Some Unbounded Domains. Nonlinear Analysis, 32, 71-85. http://dx.doi.org/10.1016/S0362-546X(97)00453-7
|
[39]
|
Wang, X. (1995) An Energy Equation for the Weakly Damped Driven Nonlinear Schrodinger Equations and Its Applications. Physica D, 88, 167-175. http://dx.doi.org/10.1016/0167-2789(95)00196-B
|
[40]
|
Bates, P.W., Lu, K. and Wang, B. (2009) Random Attractors for Stochastic Reaction-Diffusion Equations on Unbounded Domains. Journal of Differential Equations, 246, 845-869. http://dx.doi.org/10.1016/j.jde.2008.05.017
|
[41]
|
Chueshov, I. (2002) Monotone Random Systems Theory and Applications. Springer-Verlag, New York. http://dx.doi.org/10.1007/b83277
|
[42]
|
Pazy, A. (1983) Semigroup of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York. http://dx.doi.org/10.1007/978-1-4612-5561-1
|