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Lastra, A.; Malek, S.; Sanz, J.

Strongly regular multi-level solutions of singularly perturbed linear partial differential equations. (English) Zbl 1353.35033

Result. Math. 70, No. 3-4, 581-614 (2016).
Summary: 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.

Cited in 10 Documents

MSC:

35B25 Singular perturbations in context of PDEs
35C10 Series solutions to PDEs
35C20 Asymptotic expansions of solutions to PDEs
40C10 Integral methods for summability

Keywords:

formal power series; Borel-Laplace transform; Borel summability; Gevrey asymptotic expansions; strongly regular sequence; complex domain; multi-level Ramis-Sibuya theorem
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References:

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