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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Author: Bixiang Wang
Journal: Trans. Amer. Math. Soc. 363 (2011), 3639-3663
MSC (2000): Primary 37L55; Secondary 60H15, 35B40
Published electronically: February 3, 2011
MathSciNet review: 2775822
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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.

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Additional Information

Bixiang Wang
Affiliation: Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, New Mexico 87801

Keywords: Random attractor, asymptotic compactness, wave equation.
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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