title: Variational solutions and random dynamical systems to SPDEs perturbed by fractional Gaussian noise.
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: dX(t) = A(X(t))dt+Φ(t)dB (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.
authors.affiliation: School of Sciences, South China University of Technology, Guangzhou 510640, China ; School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China.
authors.forename: Caibin
authors.initials: C
authors.lastname: Zeng
authors.affiliation: School of Sciences, South China University of Technology, Guangzhou 510640, China.
authors.forename: Qigui
authors.initials: Q
authors.lastname: Yang
authors.affiliation: Department of Mathematics, Guangdong University of Education, Guangzhou 510310, China.
authors.forename: Junfei
authors.initials: J
authors.lastname: Cao
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D055585:Physical Phenomena