Titlebook: Composite Asymptotic Expansions; Augustin Fruchard,Reinhard Sch?fke Book 2013 Springer-Verlag Berlin Heidelberg 2013 Gevrey expansions.com

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,Zufallsgr??en und Verteilungen,notions of composite formal series and composite expansions of Gevrey kind play a key-role.The notion of Gevrey asymptotics has played a key-role in the classical theory of asymptotic expansions uniform in a full neighborhood of a turning point. In the present chapter, we generalize this concept to

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Historical Remarks,, Erdélyi [18]. The matching is the main subject of Eckhaus’ book [17] and the Chaps. VII and VIII of Wasow’s book [62]. In the latter book, the method is presented for linear systems of singularly perturbed differential equations.

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Book 2013 functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansion

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https://doi.org/10.1007/978-3-8351-9211-9erval containing the turning point. Such a solution will be called a .. On the other hand we show that, if there is such a local canard, then there is also a global canard. In other words, there is no phenomenon of buffer points for this kind of equation.

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https://doi.org/10.1007/978-3-658-27218-0d then attracting. In this situation, any solution with bounded initial condition at the turning point is defined and bounded on an interval containing this turning point, but this solution can have a . s. only if the initial condition has an asymptotic expansion. We will see that this necessary condition is also sufficient.

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Four Introductory Examples,d then attracting. In this situation, any solution with bounded initial condition at the turning point is defined and bounded on an interval containing this turning point, but this solution can have a . s. only if the initial condition has an asymptotic expansion. We will see that this necessary condition is also sufficient.

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