Working Paper Article Version 1 This version is not peer-reviewed

On Inner Expansions for A Singularly Perturbed Cauchy Problem with Confluent Fuchsian Singularities

Version 1 : Received: 21 April 2020 / Approved: 23 April 2020 / Online: 23 April 2020 (04:33:13 CEST)

How to cite: Malek, S. On Inner Expansions for A Singularly Perturbed Cauchy Problem with Confluent Fuchsian Singularities. Preprints 2020, 2020040401 Malek, S. On Inner Expansions for A Singularly Perturbed Cauchy Problem with Confluent Fuchsian Singularities. Preprints 2020, 2020040401

Abstract

A nonlinear singularly perturbed Cauchy problem with confluent fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time. A similar initial value problem with logarithmic reliance in time has been investigated by the author in a recent work, for which sets of holomorphic inner and outer solutions were built up and expressed as a Laplace transform with logarithmic kernel. Here, a family of holomorphic inner solutions are constructed by means of exponential transseries expansions containing infinitely many Laplace transforms with special kernel. Furthermore, asymptotic expansions of Gevrey type for these solutions relatively to the perturbation parameter are established.

Subject Areas

asymptotic expansion; Borel-Laplace transform; Cauchy problem; formal power series; integro-differential equation; partial differential equation; singular perturbation

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