Periodic measures for a class of SPDEs with regime-switching

Abstract

We use the variational approach to investigate periodic measures for a class of stochastic partial differential equations (SPDEs) with regime-switching. The hybrid system is driven by degenerate Lévy noise. We use the Lyapunov function method to study the existence of periodic measures and show the uniqueness of periodic measures by establishing the strong Feller property and irreducibility of the associated time-inhomogeneous semigroup. The main results are applied to stochastic fractional porous medium equations with regime-switching.