Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise. (15th January 2014)

• Record Type: Journal Article
• Authors: Zeng, Caibin; Yang, Qigui; Cao, Junfei
• Other Names: Prieto-Rumeau T. Academic Editor.; Saito K. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-01-15
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/601327
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ : d X ( t ) = A ( X ( t ) ) d t + Φ ( t ) d B H ( t ), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p -Laplacian equation.