{"title":"On parametric $0$-Gevrey asymptotic expansions in two levels for some linear partial $q$-difference-differential equations","authors":"Alberto Lastra, Stephane Malek","doi":"arxiv-2408.12335","DOIUrl":null,"url":null,"abstract":"A novel asymptotic representation of the analytic solutions to a family of\nsingularly perturbed $q-$difference-differential equations in the complex\ndomain is obtained. Such asymptotic relation shows two different levels\nassociated to the vanishing rate of the domains of the coefficients in the\nformal asymptotic expansion. On the way, a novel version of a multilevel\nsequential Ramis-Sibuya type theorem is achieved.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"20 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.12335","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A novel asymptotic representation of the analytic solutions to a family of
singularly perturbed $q-$difference-differential equations in the complex
domain is obtained. Such asymptotic relation shows two different levels
associated to the vanishing rate of the domains of the coefficients in the
formal asymptotic expansion. On the way, a novel version of a multilevel
sequential Ramis-Sibuya type theorem is achieved.
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