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2021 Summability in a monomial for some classes of singularly perturbed partial differential equations
Sergio A. Carrillo
Publ. Mat. 65(1): 83-127 (2021). DOI: 10.5565/PUBLMAT6512103

Abstract

The aim of this paper is to continue the study of asymptotic expansions and summability in a monomial in any number of variables, as introduced in [3, 15]. In particular, we characterize these expansions in terms of bounded derivatives and we develop Tauberian theorems for the summability processes involved. Furthermore, we develop and apply the Borel-Laplace analysis in this framework to prove the monomial summability of solutions of a specific class of singularly perturbed PDEs.

Funding Statement

Supported by the Austrian FWF-Project P 26735-N25 under P. I. Armin Rainer. Partially supported by the Ministerio de Economía y Competitividad from Spain, under the Project “Ágebra y geometría en sistemas dinámicos y foliaciones singulares” (Ref.: MTM2016-77642-C2-1-P).

Citation

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Sergio A. Carrillo. "Summability in a monomial for some classes of singularly perturbed partial differential equations." Publ. Mat. 65 (1) 83 - 127, 2021. https://doi.org/10.5565/PUBLMAT6512103

Information

Received: 2 July 2019; Revised: 16 July 2020; Published: 2021
First available in Project Euclid: 11 December 2020

MathSciNet: MR4185828
Digital Object Identifier: 10.5565/PUBLMAT6512103

Subjects:
Primary: 34M30
Secondary: 34E05

Keywords: Borel summability , monomial summability , singularly perturbed PDEs

Rights: Copyright © 2021 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.65 • No. 1 • 2021
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