PreprintArticleVersion 1Preserved in Portico This version is not peer-reviewed
Parametric asymptotic expansions and confluence for Banach valued solutions to some singularly perturbed nonlinear q-difference-differential Cauchy problem
Version 1
: Received: 11 April 2024 / Approved: 11 April 2024 / Online: 12 April 2024 (07:02:53 CEST)
How to cite:
Malek, S. Parametric asymptotic expansions and confluence for Banach valued solutions to some singularly perturbed nonlinear q-difference-differential Cauchy problem. Preprints2024, 2024040824. https://doi.org/10.20944/preprints202404.0824.v1
Malek, S. Parametric asymptotic expansions and confluence for Banach valued solutions to some singularly perturbed nonlinear q-difference-differential Cauchy problem. Preprints 2024, 2024040824. https://doi.org/10.20944/preprints202404.0824.v1
Malek, S. Parametric asymptotic expansions and confluence for Banach valued solutions to some singularly perturbed nonlinear q-difference-differential Cauchy problem. Preprints2024, 2024040824. https://doi.org/10.20944/preprints202404.0824.v1
APA Style
Malek, S. (2024). Parametric asymptotic expansions and confluence for Banach valued solutions to some singularly perturbed nonlinear q-difference-differential Cauchy problem. Preprints. https://doi.org/10.20944/preprints202404.0824.v1
Chicago/Turabian Style
Malek, S. 2024 "Parametric asymptotic expansions and confluence for Banach valued solutions to some singularly perturbed nonlinear q-difference-differential Cauchy problem" Preprints. https://doi.org/10.20944/preprints202404.0824.v1
Abstract
We investigate a singularly perturbed q-difference differential Cauchy problem with polynomial coefficients in complex time and space with quadratic nonlinearity. We construct local holomorphic solutions on sectors in the complex plane with respect to the perturbation parameter with values in some Banach space of formal power series in space with analytic coefficients on shrinking domains in time. Two aspects of these solutions are addressed. One feature concerns asymptotic expansions in the parameter for which a Gevrey type structure is unveiled. The other fact deals with confluence properties as q tends to 1. In particular the built up Banach valued solutions are shown to merge in norm to a fully bounded holomorphic map in all its arguments that solves a nonlinear partial differential Cauchy problem.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
