Ergodicity of a nonlinear stochastic reaction–diffusion equation with memory

We consider a class of semi-linear differential Volterra equations with memory terms, polynomial nonlinearities and random perturbation. For broad nonlinearities, we show that the system in concern admits unique weak solution. Also, any statistically steady state must possess regularity compatible Moreover, if sufficiently many directions are stochastically forced, employ generalized coupling approach to prove there exists invariant probability measure is exponentially attractive. This extends ergodicity results previously established Bonaccorsi et al., (2012).