Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise. (15th January 2014) - Zeng, Caibin; Yang, Qigui; Cao, Junfei
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.