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Asymptotic solutions to Fuchsian equations in several variables. (English) Zbl 0858.35004
Janeczko, Stanisław (ed.) et al., Singularities and differential equations. Proceedings of a symposium, Warsaw, Poland. Warsaw: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 33, 351-363 (1996).
Summary: The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors [Math. Nachr. 171, 283-301 (1995; Zbl 0842.32006)]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.
For the entire collection see [Zbl 0840.00028].
MSC:
35A20 Analyticity in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
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