## Asymptotic behavior of stochastic wave equations with critical exponents on $\mathbb {R}^3$

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**363**(2011), 3639-3663 Request permission

## Abstract:

The existence of a random attractor in $H^1(\mathbb {R}^3) \times L^2(\mathbb {R}^3)$ is proved for the damped semilinear stochastic wave equation defined on the entire space $\mathbb {R}^3$. The nonlinearity is allowed to have a cubic growth rate which is referred to as the critical exponent. The uniform pullback estimates on the tails of solutions for large space variables are established. The pullback asymptotic compactness of the random dynamical system is proved by using these tail estimates and the energy equation method.## References

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## Additional Information

**Bixiang Wang**- Affiliation: Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, New Mexico 87801
- MR Author ID: 314148
- Email: bwang@nmt.edu
- Received by editor(s): May 1, 2009
- Received by editor(s) in revised form: November 2, 2009
- Published electronically: February 3, 2011
- Additional Notes: The author was supported in part by NSF grant DMS-0703521
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**363**(2011), 3639-3663 - MSC (2000): Primary 37L55; Secondary 60H15, 35B40
- DOI: https://doi.org/10.1090/S0002-9947-2011-05247-5
- MathSciNet review: 2775822