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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01 May 1980
TL;DR: In this paper, a generalized class of singularly perturbed systems is considered and conditions are presented under which the solution of a single point perturbed system converges with the parameter, and a geometric decomposition that preserves continuity about the singular point is derived.
Abstract: : Existing results in descriptor variable theory are interpreted geometrically. New results are obtained concerning linear feedback and pole placement in such systems. Descriptor variable systems are viewed as limits of singularly perturbed systems. It is shown that some important singularly perturbed systems cannot be treated effectively with standard techniques. Hence, a generalized class of singularly perturbed systems is considered. A geometric decomposition that preserves continuity about the singular point is derived. Conditions are presented under which the solution of a singularly perturbed system converges with the parameter. Miscellaneous structural properties are established with applications to the quadratic regulator problem. (Author)
26 citations
TL;DR: In this article, the authors considered the vertical flow of an internally heated Boussinesq fluid in a vertical channel with viscous dissipation and pressure work, and they obtained two solutions; the expected solution with no flow and the second adiabatic solution with temperatures less than the wall temperature and a large downward velocity.
26 citations
TL;DR: In this paper, an asymptotically consistent two-dimensional theory is developed to help elucidate dynamic response in finitely deformed layers, where the layers are composed of incompressible elastic material, with the theory appropriate for long wave motion associated with the fundamental mode and derived in respect of the most general appropriate strain energy function.
Abstract: An asymptotically consistent two–dimensional theory is developed to help elucidate dynamic response in finitely deformed layers. The layers are composed of incompressible elastic material, with the theory appropriate for long–wave motion associated with the fundamental mode and derived in respect of the most general appropriate strain energy function. Leading–order and refined higher–order equations for the mid–surface deflection are derived. In the case of zero normal initial static stress and in–plane tension, the leading–order equation reduces to the classical membrane equation, with its refined counterpart also being obtained. The theory is applied to a one–dimensional edge loading problem for a semi–infinite plate. In doing so, the leading– and higher–order governing equations are used as inner and outer asymptotic expansions, the latter valid within the vicinity of the associated quasi–front. A solution is derived by using the method of matched asymptotic expansions.
26 citations
TL;DR: In this paper, the singularly perturbed boundary value problem for a system of equations with different powers of a small parameter is considered in the one-dimensional case, and the asymptotic behavior and existence of a solution with an internal transition layer are analyzed.
Abstract: A singularly perturbed boundary value problem for a system of equations with different powers of a small parameter is considered in the one-dimensional case. The asymptotic behavior and existence of a solution with an internal transition layer are analyzed. The asymptotics are substantiated using the asymptotic method of differential inequalities.
26 citations
TL;DR: In this paper, a class of coupled equations for composite problems in elasticity theory for non-uniform bodies was studied, where the approximate solutions, constructed using the method described in /1/ by reducing the problem to a finite system of algebraic equations, are two-sided asymptotically exact in terms of the characteristic geometric parameter.
26 citations