| 作者： | Alberto Lastra, Stephane Malek |
| 作者单位： |
1Univ. de Alcala, Madrid, Spain 2Univ. of Lille 1, France |
| 刊名： | Electronic Journal of Differential Equations, 2018, Vol.2018 (46,), pp.1-89 |
| 来源数据库： | Directory of Open Access Journals |
| 关键词： | Asymptotic expansion; Borel-Laplace transform; Fourier transform; Cauchy problem; Formal power series; Nonlinear integro-differential equation; Nonlinear partial differential equation; Singular perturbation; |
| 原始语种摘要： | We study a singularly perturbed PDE with cubic nonlinearitydepending on a complex perturbation parameter $\epsilon$.This is a continuation of the precedent work [22] by thefirst author. We construct two families of sectorial meromorphicsolutions obtained as a small perturbation in $\epsilon$ of twobranches of an algebraic slow curve of the equation in time scale.We show that the nonsingular part of the solutions of each familyshares a common formal power series in $\epsilon$ as Gevrey asymptoticexpansion which might be different one to each other, in general. |