Variational solutions and random dynamical systems to SPDEs perturbed by fractional Gaussian noise
Summary: 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 \(\Phi:dX(t)=A(X(t))dt+\Phi(t)dB^H(t)\), 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.
scientific article; zbMATH DE number 6529680
scientific article