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Differential Equations in Banach Algebras
Doklady Mathematics, 2020In 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, 1970Abstract : 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, 2022The 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, 2000Summary: 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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