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Variational solutions and random dynamical systems to SPDEs perturbed by fractional Gaussian noise
Caibin Zeng1, Qigui Yang2, Junfei Cao3
1School of Sciences, South China University of Technology, Guangzhou 510640, China ; School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China.
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.
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