Random attractors via pathwise mild solutions for stochastic parabolic evolution equations

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2021
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Kuehn, Christian
Sonner, Stefanie
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Zusammenfassung

We investigate the longtime behavior of stochastic partial differential equations (SPDEs) with differential operators that depend on time and the underlying probability space. In particular, we consider stochastic parabolic evolution problems in Banach spaces with additive noise and prove the existence of random exponential attractors. These are compact random sets of finite fractal dimension that contain the global random attractor and are attracting at an exponential rate. In order to apply the framework of random dynamical systems, we use the concept of pathwise mild solutions.

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Fachgebiet (DDC)
510 Mathematik
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Stochastic parabolic evolution equations, Pathwise mild solution, Random attractors, Fractal dimension
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ISO 690KUEHN, Christian, Alexandra BLESSING-NEAMTU, Stefanie SONNER, 2021. Random attractors via pathwise mild solutions for stochastic parabolic evolution equations. In: Journal of Evolution Equations. Springer. 2021, 21(2), pp. 2631-2663. ISSN 1424-3199. eISSN 1424-3202. Available under: doi: 10.1007/s00028-021-00699-x
BibTex
@article{Kuehn2021-06Rando-57999,
  year={2021},
  doi={10.1007/s00028-021-00699-x},
  title={Random attractors via pathwise mild solutions for stochastic parabolic evolution equations},
  number={2},
  volume={21},
  issn={1424-3199},
  journal={Journal of Evolution Equations},
  pages={2631--2663},
  author={Kuehn, Christian and Blessing-Neamtu, Alexandra and Sonner, Stefanie}
}
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