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Effect of rotational field on thermo-acoustic and optical wave propagation in hydrodynamic semiconductors. [PDF]
Sci RepAlshehri HM, Lotfy K.
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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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Solvability of General Differential Algebraic Equations
SIAM Journal on Scientific Computing, 1995Summary: In the last few years there has been considerable research on differential algebraic equations (DAE) \(f(t,x,x') = 0\) where \(f_{x'}\) is identically singular. Most of this effort has focused on computing a solution that is assumed to exist. That is, the DAE is assumed solvable.
Stephen L. Campbell, E. Griepentrog
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Solutions of Linear Differential Algebraic Equations
SIAM Review, 1998Summary: The authors show how to solve inhomogeneous linear differential algebraic systems with constant coefficients.
Mazi Shirvani, Joseph W.-H. So
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Differential-Algebraic Equations
Oberwolfach Reports, 2007The topic of Differential Algebraic Equations (DAEs) began to attract significant research interest in applied and numerical mathematics in the early 1980's. Today, a quarter of a century later, DAEs are an independent field of research, which is gaining in importance and becoming of increasing interest for both applications and mathematical theory.
Stephen L. Campbell +3 more
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Differential — Algebraic Equations
2003Differential — algebraic equations (DAE) differ from other problems with solutions given by smooth and continuous parametric sets. They combine specifics of the nonlinear algebraic or transcendental equations with those of ODE. Correct formulation of the Cauchy problem for such equations requires solution of a system of nonlinear equations.
V. I. Shalashilin, E. B. Kuznetsov
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