Non-autonomous and random attractors for delay random semilinear equations without uniqueness.

*(English)*Zbl 1155.60025This article investigates the asymptotic behaviour of random and stochastic evolution equations with infinite delays when uniqueness of solutions for these equations is not required. The abstract theory is applied to a random reaction-diffusion equation with memory or delay terms defined on the complete past up to time $-\infty $.

In particular the authors study the existence and uniqueness of pullback and random attractors associated to multivalued non-autonomous and random dynamical systems, which are generated by the globally defined solutions of the equations. The authors address also the problem that the solution operators are only asymptotically compact.

Reviewer: Dirk Blömker (Augsburg)

##### MSC:

60H15 | Stochastic partial differential equations |

35K40 | Systems of second-order parabolic equations, general |

35R60 | PDEs with randomness, stochastic PDE |