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Inertial Manifolds for Random Differential Equations

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Probability and Partial Differential Equations in Modern Applied Mathematics

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 140))

Abstract

The intention of the article is to show the existence of inertial manifolds for random dynamical systems generated by infinite dimensional random evolution equations. To find these manifolds we formulate a random graph transform. This transform allows us to introduce a random dynamical system on graphs. A random fixed point of this system defines the graph of the inertial manifold. In contrast to other publications dealing with these objects we also suppose that the linear part of such an evolution equation contains random operators. To deal with these objects we apply th e multiplicative ergodic theorem. The key assumption for the existence of an inertial manifold is an ω-wise gap condition.

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Author information

Authors and Affiliations

  1. Mathematical Institute, University of Paderborn, Warburger StraBe 100, 33098, Paderborn, Germany

    BjÖrn Schmalfuss

Authors
  1. BjÖrn Schmalfuss
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Oregon State University, Covallis, OR, 97331, USA

    Edward C. Waymire

  2. Department of Applied Mathematics, Illionis Institute of Technology, Chicago, IL, 60616, USA

    Jinqiao Duan

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Schmalfuss, B. (2005). Inertial Manifolds for Random Differential Equations. In: Waymire, E.C., Duan, J. (eds) Probability and Partial Differential Equations in Modern Applied Mathematics. The IMA Volumes in Mathematics and its Applications, vol 140. Springer, New York, NY. https://doi.org/10.1007/978-0-387-29371-4_14

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