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On the Reduction of Coercive Singular Perturbations to Regular Perturbations
1989Summary: It is shown that for a coercive singular perturbation \({\mathcal A}^{\epsilon}\) appearing in the linear elasticity theory, an appropriate choice of a reducing operator \(S^{\epsilon}\) leads to the asymptotic relation: \(S^{\epsilon}{\mathcal A}^{\epsilon}={\mathcal A}^ 0+\epsilon Q^{\epsilon}\), where \({\mathcal A}^ 0\) is the reduced ...
Frank, L. S., Heijstek, J. J.
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On Singular Perturbations, Especially Matching
SIAM Review, 1994Among fifty very strong minisymposia at ICIAM 91 (cf. O'Malley (1992)), that on the Historical Development of Singular Perturbation Concepts, somewhat surprisingly, seemed to be the most popular. In retrospect, this was certainly due to both its accomplished participants and to the importance of asymptotic analysis throughout contemporary applied ...
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Formal Approximations and Singular Perturbations
SIAM Review, 1977The problem of proving the validity of a formal approximation as an asymptotic approximation in singular perturbation problems is studied in a general formulation.
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An Asymptotic Approximation for Singular Perturbations
SIAM Journal on Applied Mathematics, 1983The topic of the paper under review is to discuss a practical approach to the approximate solution of singularly perturbed systems of d.e.'s of the type \((1)_{\mu} \dot x=f(x,y,t), \mu \dot y=g(x,y,t)\) with \(\mu\) being the small parameter. As usual it is assumed that the reduced system \((1)_ 0\) admits a reduced manifold of solutions with strong ...
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Expansions for Singular Perturbations
IMA Journal of Applied Mathematics, 1971openaire +2 more sources
Anisotropic singular perturbations of hyperbolic problems
Applied Mathematics and Computation, 2011Senoussi Guesmia +1 more
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Slow State Variables Feedback Stabilization for Semi-Markov Jump Systems With Singular Perturbations
IEEE Transactions on Automatic Control, 2018Hao Shen +2 more
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