Topic
Method of matched asymptotic expansions
About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.
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TL;DR: For singularly perturbed parabolic problems, asymptotic expansions of time-periodic solutions with boundary layers in a neighborhood of interval's endpoints are constructed and justified in the case where the degenerate equation has a double or a triple root.
Abstract: For singularly perturbed parabolic problems, asymptotic expansions of time-periodic solutions with boundary layers in a neighborhood of interval’s endpoints are constructed and justified in the case where the degenerate equation has a double or a triple root.
23 citations
Book•
16 Dec 2012
TL;DR: In this article, Gevrey Theory is applied to composite expansions and Singularly Perturbed Differential Equations (SPDE) in the context of singularly perturbed differential equations.
Abstract: Four Introductory Examples.- Composite Asymptotic Expansions: General Study.- Composite Asymptotic Expansions: Gevrey Theory.- A Theorem of Ramis-Sibuya Type.- Composite Expansions and Singularly Perturbed Differential Equations.- Applications.- Historical Remarks.- References.- Index.
23 citations
TL;DR: A direct approach to the Lur'e problem for singularly perturbed systems (SPS) is proposed, and the feedback connection between the linear and nonlinear parts of SPS is allowed to depend essentially on both the slow and the fast variables.
Abstract: A direct approach to the Lur'e problem for singularly perturbed systems (SPS) is proposed. In contrast to previous results, the feedback connection between the linear and nonlinear parts of SPS is allowed to depend essentially on both the slow and the fast variables. The Lur'e problem for multiparameter SPS is studied by the same framework.
23 citations
TL;DR: In this article, the qualitative properties of solutions of the perfect-fluid Einstein field equations in the case of spherical symmetry were investigated, and exact solutions were obtained and the asymptotic behaviour of the solutions were fully studied in these important subcases.
Abstract: The perfect-fluid Einstein field equations in the case of spherical symmetry reduce to an autonomous system of ordinary differential equations when a spacetime is assumed to admit a kinematic self-similarity (of either the second or zeroth kind). The qualitative properties of solutions of this system of equations, and in particular their asymptotic behaviour, are investigated. The geodesic subcase and a subcase containing the static models are examined in detail. In particular, exact solutions are obtained and the asymptotic behaviour of the solutions is fully studied in these important subcases. Exact solutions admitting a homothetic vector are found to play an important role in describing the asymptotic behaviour of the kinematic self-similar models.
23 citations
TL;DR: In this paper, the authors established a general formula for the translational speed of a counter-rotating vortex pair, valid for thick cores, moving in an incompressible fluid with and without viscosity.
23 citations