Affiliation:
1. University of Lille, Lille, France
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 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
and
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
on bounded sectors at the origin.
Subject
Applied Mathematics,Analysis
Cited by
1 articles.
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