Abstract
We first present the existence of a random attractor of a stochastic dynamical system generated by a damped nonlinear wave equation with white noise under the Dirichlet boundary condition and estimate the explicit bound of the random attractor. And then we obtain an estimate of the upper bound of the Hausdorff dimension of the random attractor. The obtained upper bound of the Hausdorff dimension decreases as the damping grows and it is uniformly bounded if the derivative of nonlinearity is bounded; moreover, in this case, the upper bound of the Hausdorff dimension of the random attractor is just the upper bound of the Hausdorff dimension of the global attractor for the corresponding deterministic system without noise.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
