一类奇摄动偏微分方程的单项可和性

Pub Date : 2018-03-18 DOI:10.5565/publmat6512103

S. A. Carrillo

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引用次数: 4

摘要

本文的目的是完成对任意数量变量的单项式的渐近展开式和可和性的研究。特别地，我们用有界导数来描述这些展开式，并为所涉及的可和过程开发了陶培尔定理。进一步，我们在此框架下发展并应用了Borel-Laplace分析，证明了一类特定奇摄动偏微分方程解的单项式可和性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Summability in a monomial for some classes of singularly perturbed partial differential equations

The aim of this paper is to complete the study of asymptotic expansions and summability in a monomial in any number of variables. 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.

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