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Almost Periodic Solutions of Navier–Stokes–Ohm Type Equations in Magneto-Hydrodynamics

  • Evagelia S. Athanasiadou
  • Vasileios F. Dionysatos
  • Panagiotis N. KoumantosEmail author
  • Panaiotis K. Pavlakos
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 91)

Abstract

In this paper we construct (Bohl-Bohr- and Stepanoff-) almost periodic solutions of an evolution equation of the form \(\left ( \frac{d} {dt} + A\right )x(t) = F(t,x(t))\), \(t \in \mathbb{R}\), describing the velocity and the magnetic field of a viscous incompressible homogeneous ideal plasma in magneto-hydrodynamics. By − A it is denoted the infinitesimal generator of a C o-semigroup \({e}^{-tA}\), \(t \in {\mathbb{R}}^{+}\) of operators acting on an ordered Hilbert space E and \(F: \mathbb{R} \times E \rightarrow E\) is a given function. We also examine the case of the construction of positive almost periodic solutions.

Keywords

Evolution equation Analytic semigroups Strong and classical solutions Ordered Banach spaces Magneto-hydrodynamics 

Mathematics Subject Classification (2010):

34K30 35R10 47H07 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Evagelia S. Athanasiadou
    • 1
  • Vasileios F. Dionysatos
    • 1
  • Panagiotis N. Koumantos
    • 1
    • 2
    Email author
  • Panaiotis K. Pavlakos
    • 1
  1. 1.Mathematics DepartmentNational and Kapodistrian University of AthensAthensGreece
  2. 2.Physics DepartmentNational and Kapodistrian University of AthensAthensGreece

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