Version 1
: Received: 30 January 2023 / Approved: 31 January 2023 / Online: 31 January 2023 (10:17:51 CET)
How to cite:
Malek, S. Gevrey Asymptotics for Logarithmic Type Solutions to Singularly Perturbed Problems with Nonlocal Nonlinearities. Preprints.org2023, 2023010582. https://doi.org/10.20944/preprints202301.0582.v1
Malek, S. Gevrey Asymptotics for Logarithmic Type Solutions to Singularly Perturbed Problems with Nonlocal Nonlinearities. Preprints.org 2023, 2023010582. https://doi.org/10.20944/preprints202301.0582.v1
Cite as:
Malek, S. Gevrey Asymptotics for Logarithmic Type Solutions to Singularly Perturbed Problems with Nonlocal Nonlinearities. Preprints.org2023, 2023010582. https://doi.org/10.20944/preprints202301.0582.v1
Malek, S. Gevrey Asymptotics for Logarithmic Type Solutions to Singularly Perturbed Problems with Nonlocal Nonlinearities. Preprints.org 2023, 2023010582. https://doi.org/10.20944/preprints202301.0582.v1
Abstract
We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter and singular in a complex time variable at the origin. These equations combine differential operators of Fuchsian type in time and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the complex parameter known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic type functions in time and are bounded holomorphic in space. A set of logarithmic type solutions are shaped by means of Laplace transforms relatively to time and parameter and Fourier integrals in space. Furthermore, a formal logarithmic type solution is modeled which represents the common asymptotic expansion of Gevrey type of the genuine solutions with respect to the complex parameter on bounded sectors at the origin.
Keywords
Asymptotic expansion; Borel-Laplace transform; Fourier transform; initial value problem; formal power series; formal monodromy; singular perturbation
Subject
Computer Science and Mathematics, Analysis
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.
