Well-posedness and dynamics of a fractional stochastic integro-differential equation. (English) Zbl 1378.37091
Summary: In this paper, we investigate the well-posedness and dynamics of a fractional stochastic integro-differential equation describing a reaction process depending on the temperature itself. Existence and uniqueness of solutions of the integro-differential equation is proved by the Lumer-Phillips theorem. Besides, under appropriate assumptions on the memory kernel and on the magnitude of the nonlinearity, the existence of random attractor is achieved by obtaining first some a priori estimates. Moreover, the random attractor is shown to have finite Hausdorff dimension.
MSC:
| 37H10 | Generation, random and stochastic difference and differential equations |
| 35R09 | Integro-partial differential equations |
| 35R11 | Fractional partial differential equations |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 37G35 | Dynamical aspects of attractors and their bifurcations |
Keywords:
fractional stochastic integro-differential equation; random attractor; Lumer-Phillips theorem; Hausdorff dimension; a priori estimatesReferences:
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