一类奇异非线性q-差分微分Cauchy问题的渐近性和收敛性

Q3 Mathematics

Abstract and Applied Analysis Pub Date : 2022-08-08 DOI:10.1155/2022/9637628

S. Malek

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引用次数: 0

摘要

我们研究了一组非线性q−差分微分柯西问题，这些问题是作者最近研究的包含扩张q−差算子的线性柯西问题和包含收缩q−差运算符的拟线性Kowalevski型问题的耦合。我们建立了这些问题的局部全纯解。探讨了这些解决方案的两个方面。一个方面涉及复时间变量中的渐近展开，其表现出混合型Gevrey和q−Gevrey结构。另一个特征涉及当q>1趋向于1时这些解的汇合问题。

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Asymptotics and Confluence for a Singular Nonlinear q -Difference-Differential Cauchy Problem

We examine a family of nonlinear q − difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q − difference operators, recently investigated by the author, and quasilinear Kowalevski type problems that involve contraction q − difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q − Gevrey structure are exhibited. The other feature concerns the problem of confluence of these solutions as q > 1 tends to 1.

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来源期刊

Abstract and Applied Analysis 数学-数学

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

3.5 months

期刊介绍： Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.