Strongly regular multi-level solutions of singularly perturbed linear partial differential equations

Alberto Lastra; Stéphane Malek; Javier Sanz

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arXiv · 1502.07222

Strongly regular multi-level solutions of singularly perturbed linear partial differential equations

Alberto Lastra·Stéphane Malek·Javier Sanz

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Abstract

We study the asymptotic behavior of the solutions related to a family of singularly perturbed partial differential equations in the complex domain. The analytic solutions are asymptotically represented by a formal power series in the perturbation parameter. The geometry of the problem and the nature of the elements involved in it give rise to different asymptotic levels related to the so-called strongly regular sequences. The result leans on a novel version of a multi-level Ramis-Sibuya theorem.

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Alberto Lastra, Stéphane Malek, Javier Sanz. 2015-02-25. Strongly regular multi-level solutions of singularly perturbed linear partial differential equations. https://arxiv.org/abs/1502.07222

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