Download Navier-Stokes Equations II: Theory and Numerical Methods by Heywood J.G. PDF

By Heywood J.G.

Court cases of a convention Held in Oberwolfach, Germany, August 18-24, 1991

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Additional resources for Navier-Stokes Equations II: Theory and Numerical Methods

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For i = 1, . . 11d) Controllability of Linear Differential-Algebraic Systems—A Survey Nκi x˙f [i] (t) = xc (t) for i = 1, . . 11e) x˙c (t) = Ac xc (t). 10) is a normal form. g. 10) becomes a canonical form. g. [147, Sect. 2]). This system has furthermore the properties of being R-controllable, and both controllable and stabilizable in the behavioral sense. 11b) corresponds to an underdetermined system with zero dimensional input space. 11a). 4, the unique solution zob[i] = 0. Hence, B [γ ] [Lγ ,Kγ ,eγi i ] i = {0}.

Then the following holds true: 38 T. Berger and T. Reis [E, A] is completely stabilizable if, and only if, (α) = 0, γ = (1, . . , 1) and σ (As ) ⊆ C− . strongly stabilizable α = (1, . . , 1), γ = (1, . . , 1) and σ (As ) ⊆ C− . stabilizable in the behavioral sense σ (As ) ⊆ C− . autonomous (β) = 0. completely stable (α) = 0, (β) = 0, γ = (1, . . , 1) and σ (As ) ⊆ C− . strongly stable stable in the behavioral sense α = (1, . . , 1), (β) = 0, γ = (1, . . , 1) and σ (As ) ⊆ C− . (β) = 0, σ (As ) ⊆ C− .

11b) corresponds to an underdetermined system with zero dimensional input space. 11a). 4, the unique solution zob[i] = 0. Hence, B [γ ] [Lγ ,Kγ ,eγi i ] i = {0}. i [γ ] The system [Lγi , Kγi , eγi i ] is therefore completely controllable if, and only if, γi = 1. In the case where γi > 1, this system is not even impulse control[γ ] lable. However, independent of γi , [Lγi , Kγi , eγi i ] is R-controllable, and both controllable and stabilizable in the behavioral sense. (iv) Again, we have B[K δi ,Lδi ,0δi ,0 ] = {0}, whence, in dependence on δi , we can infer the same properties as in (iii).

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