Detalhes do Documento

Some results on 3D delay Kelvin–Voigt–Brinkman–Forchheimer equations with non-autonomous forcing term and operator type multiplicative white noise are analyzed. First, the existence, uniqueness and backward compactness of pullback random attractors is proved by the backward flattening of solutions and Ascoli-Arzelà theorem. Then we study three types of stability of pullback random attractors: (i) The backward stability of pullback random attractors as the time parameter tends to negative infinity; (ii) The asymptotic autonomous stability of pullback random attractors; (iii) The non-delay stability of pullback random attractors as the delay parameter approaches zero. Since the high regularity of the solution is not easy established, we use the method of the spectrum decomposition to prove the backward asymptotic compactness of the solution operator.