Asymptotic behaviour of a class of nonlinear heat conduction problems with memory effects

In this paper, we investigate the existence and uniqueness problem for the solutions to a class of semilinear stochastic Volterra equations which arise in the theory of heat conduction with memory eects, where the heat source depends on the solution via a dissipative term. Further, we analyse the asymptotic behaviour of the solution and we prove the existence of a ergodic invariant measure