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Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations

Tom 60 / 2003

Norbert Koksch, Stefan Siegmund Banach Center Publications 60 (2003), 27-48 MSC: 34C30, 34D45, 34G20, 35B42, 37L25 DOI: 10.4064/bc60-0-2

Streszczenie

In this paper we summarize an abstract approach to inertial manifolds for nonautonomous dynamical systems. Our result on the existence of inertial manifolds requires only two geometrical assumptions, called cone invariance and squeezing property, and some additional technical assumptions like boundedness or smoothing properties. We apply this result to processes (two-parameter semiflows) generated by nonautonomous semilinear parabolic evolution equations.

Autorzy

  • Norbert KokschDepartment of Mathematics, Technical University Dresden, 01062
    Dresden, Germany
    e-mail
  • Stefan SiegmundDepartment of Mathematics, University of California
    Berkeley, CA 94720, USA
    e-mail

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