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

Stéphane Malek

Abstract and Applied Analysis, 2023, vol. 2023, issue 1

Abstract: 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 the complex plane with a nonlocal operator acting on the parameter ϵ 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 t and ϵ and Fourier integrals in space. Furthermore, a formal logarithmic‐type solution is modeled which represents the common asymptotic expansion of the Gevrey type of the genuine solutions with respect to ϵ on bounded sectors at the origin.

Date: 2023
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https://doi.org/10.1155/2023/3025513

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2023:y:2023:i:1:n:3025513

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