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abstract:
In this talk we will report on some results concerning the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system perturbed by either additive or multiplicative noise.
We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true.
Using the theory of multi-valued random dynamical systems we are able to prove the existence of a random compact global attractor in both cases. |
