Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 28 July 2021 / Approved: 29 July 2021 / Online: 29 July 2021 (10:32:20 CEST)
Version 2 : Received: 21 March 2022 / Approved: 22 March 2022 / Online: 22 March 2022 (11:41:03 CET)

How to cite: Malek, S. Asymptotics and Confluence for a Singular Nonlinear Q-Difference-Differential Cauchy Problem. Preprints 2021, 2021070645 (doi: 10.20944/preprints202107.0645.v2). Malek, S. Asymptotics and Confluence for a Singular Nonlinear Q-Difference-Differential Cauchy Problem. Preprints 2021, 2021070645 (doi: 10.20944/preprints202107.0645.v2).

Abstract

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 quasi-linear 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 is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

Keywords

asymptotic expansion; confluence; formal power series; partial differential equation; q-difference equation

Subject

MATHEMATICS & COMPUTER SCIENCE, Analysis

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