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The Linearized Nonstationary Theory

  • Hermann Sohr
Chapter
  • 1.8k Downloads
Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

Abstract

Let Ω \(\Omega \subseteq {\mathbb{R}^n}\) be an arbitrary domain with n ≥ 2 and boundary ∂Ω. In the linear time dependent theory we admit arbitrary dimensions n ≥ 2. Let 0 < T ≤ ∞. Then [0, T) is called the time interval. The case T = ∞ is admitted. We call t ∈ [0, T) the time variable and x = (x 1x n ) ∈ Ω the spaces variables. for each scalar or vector function
$$ v:(t,x) \mapsto v(t,x),t \in [0,T),x \in \Omega $$
let v(t) = v(t, ·) be the function xv (t,x) only in the space variables with fixed t.

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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Hermann Sohr
    • 1
  1. 1.Fachbereich Mathematik/InformatikUniversität PaderbornPaderbornSwitzerland

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