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On Algebraic Differential Equations

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Differential Equations in Banach Algebras

Doklady Mathematics, 2020
In a complex Banach algebra \(\mathbb{B}\) the ordinary linear differential equation \[ \mathbf{x}^{(n)} + \mathbf{p}_1\mathbf{x}^{(n-1)} + \dots + \mathbf{p}_{n-1}\dot{\mathbf{x}} + \mathbf{p}_ n \mathbf{x} = 0 \tag{1} \] with constant coefficients is considered.
Perov, A. I., Kostrub, I. D.
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On the Reduction of Differential Equations to Algebraic Equations

SIAM Journal on Mathematical Analysis, 1970
Abstract : Techniques based upon elementary group theory for the reduction of a given system of partial differential equations to a system of differential equations in fewer independent variables are extended in this report. Specifically, the extension is aimed at reducing a given system to a system of algebraic equations. (Author)
Moran, M. J., Gaggioli, R. A.
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On output stabilizability of differential–algebraic equations

Systems & Control Letters, 2022
The author studies output stabilizability of differential-algebraic systems. Two different notions of stability, an asymptotic one and one based on the \(\mathrm{L}^q\)-norm of the output are compared and shown be equivalent. To introduce the use of the main concepts of output injection and the Kalman observability decomposition, the author begins with
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A Differentiation Index for Partial Differential-Algebraic Equations

SIAM Journal on Scientific Computing, 2000
Summary: A differentiation index for nonlinear partial differential-algebraic equations is presented. Determination of the differentiation index with respect to a direction in the space of independent variables uncovers all equations that must be satisfied by the Cauchy data on the hyperplane orthogonal to that direction.
Wade S. Martinson, Paul I. Barton
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