Gevrey Asymptotics for Logarithmic-Type Solutions to Singularly Perturbed Problems with Nonlocal Nonlinearities

• Published in: Abstract and applied analysis Vol. 2023; pp. 1 - 42
• Main Author: Malek, Stéphane
• Format: Journal Article
• Language: English
• Published: New York Hindawi 2023; John Wiley & Sons, Inc; Hindawi Limited
• Subjects: Asymptotic series; Differential equations, Partial; Functions (mathematics); Logarithms; Mathematical research; Nonlinear differential equations; Nonlinear theories; Nonlinearity; Numbers; Operators (mathematics); Ordinary differential equations; Parameters; Partial differential equations; Polynomials; France

We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter ϵ and singular in a complex time variable t at the origin. These equations combine differential operators of Fuchsian type in time t and space derivatives on horizontal strips in...