Limiting dynamics for stochastic wave equations

Journal of Differential Equations

Volumn 244, Issue 1, 2008, Pages 1-23

  Lv, Yan ^a   Wang, Wei ^b  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b NANJING UNIVERSITY   (China)

Author keywords

Random attractor; Random dynamical system; Singular perturbation; Stationary solution; Stochastic wave equation; Tightness

Indexed keywords

EID: 36048975698     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2007.10.009     Document Type: Article

References (26)

1. Arnold L. Random Dynamical Systems (1998), Springer-Verlag, New York/Berlin
2. Caraballo T., Langa J.A., and Robinson J.C. Upper semicontinuity of attractors for small random perturbations of dynamical systems. Comm. Partial Differential Equations 23 (1998) 1557-1581
3. Cerrai S., and Freidlin M. On the Smoluchowski-Kramers approximation for a system with an infinite number of degrees of freedom. Probab. Theory Related Fields 135 3 (2006) 363-394
4. Chow P. Stochastic wave equation with polynomial nonlinearity. Ann. Appl. Probab. 12 1 (2002) 361-381
5. Chow P., Kohler W., and Papanicolaou G. Multiple Scattering and Waves in Random Media (1981), North-Holland, Amsterdam
6. Cheban D. Global Attractors of Nonautonomous Dissipative Dynamical Systems. Interdiscip. Math. Sci. vol. 1 (2004), World Scientific
7. Crauel H., and Flandoli F. Attractor for random dynamical systems. Probab. Theory Related Fields 100 (1994) 365-393
8. Crauel H., Debussche A., and Flandoli F. Random attractors. J. Dynam. Differential Equations 9 (1997) 307-341
9. Duan J., Lu K., and Schmalfuß B. Invariant manifolds for stochastic partial differential equations. Ann. Probab. 31 4 (2003) 2109-2135
10. E W., Li X., and Vanden-Eijnden E. Some recent progress in multiscale modeling. Multiscale Modelling and Simulation. Lect. Notes Comput. Sci. Eng. vol. 39 (2004), Springer-Verlag, Berlin 3-21
11. Fan X.M. Random attractor for a damped sine-Gordon equation with white noise. Pacific J. Math. 216 1 (2004) 63-76
12. Fabrie P., Galusinski C., Miranville A., and Zelik S. Uniform exponential attractors for a singularly perturbed damped wave equation. Discrete Contin. Dyn. Syst. Ser. A 10 1-2 (2004) 211-238
13. Hale J.K., and Rauge G. Upper semicontinuity of the attractor for a singular perturbed hyperbolic equation. J. Differential Equations 73 2 (1988) 197-215
14. Hale J.K. Asymptotic Behavior of Dissipative Systems (1988), Amer. Math. Soc., Providence, RI
15. In: Imkeller P., and Monahan A. (Eds). Stochastic climate dynamics, a Special Issue in the journal. Stoch. Dyn. 2 3 (2002)
16. Lions J.L. Quelques méthodes de résolution des problèmes non linéaires (1969), Dunod, Paris
17. Da Prato G., and Zabczyk J. Stochastic Equations in Infinite Dimensions (1992), Cambridge Univ. Press
18. Ruelle D. Characteristic exponents for a viscous fluid subjected to time dependent forces. Comm. Math. Phys. 93 (1984) 285-300
19. B. Schmalfuß, Backward cocycles and attractors of stochastic differential equations, in: V. Reitmann, T. Riedrich, N. Koksch (Eds.), International Seminar on Applied Mathematics-Nonlinear Dynamics: Attractor Approximation and Global Behaviour, 1992, pp. 185-192
20. Sell G.R., and You Y. Dynamics of Evolutionary Equations (2002), Springer-Verlag, New York
21. Reed M., and Simon B. Methods of Modern Mathematical Physics II (1975), Academic Press, New York
22. Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. second ed. (1997), Springer-Verlag, New York
23. Temam R., and Miranville A. Mathematical Modeling in Continuum Mechanics. second ed. (2005), Cambridge Univ. Press, Cambridge
24. In: Waymire E., and Duan J. (Eds). Probability and Partial Differential Equations in Modern Applied Mathematics. IMA vol. 140 (2005), Springer-Verlag, New York
25. Whitham G. Linear and Nonlinear Waves (1974), Wiley, New York
26. Zhou S.F., Yin F.Q., and OuYang Z.G. Random attractor for damped nonlinear wave equations with white noise. SIAM J. Appl. Dyn. Syst. 4 4 (2005) 883-903