Random attractors for non-autonomous stochastic wave equations with nonlinear damping and white noise

Abstract

Abstract This paper is concerned with the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with additive white noise, for which the nonlinear damping has a critical cubic growth rate. By showing the pullback asymptotic compactness of the stochastic dynamic systems, we prove the existence of a random attractor in H 0 1 × L 2 $H_{0}^{1}\times L^{2}$ .

Keywords

• Random attractors
• Additive white noise
• Nonlinear damping
• Non-autonomous stochastic wave equation