Asymptotic behavior of stochastic wave equations with critical exponents on $\mathbb{R}^{3}$
By Bixiang Wang. 2008
108 citations recorded by the source corpus.
The existence of a random attractor in H 1 (ℝ 3 ) x L 2 (ℝ 3 ) is proved for the damped semilinear stochastic wave equation defined on the entire space 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.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8a39aae50226d79c58e385f146ad7f7d79a94473
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In Computational Theory and Mathematics
In Control and Systems Engineering
- Bixiang Wang
- Kening Lu
- Shengfan Zhou
- Anhui Gu
- Xiaohu Wang
- Peter W. Bates
- Andrew L. Krause
- Yangrong Li