Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity
 作者： Alberto Lastra,  Stephane Malek 作者单位： 1Univ. de Alcala, Madrid, Spain2Univ. 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.

• multiscale　通用换算
• singular　奇异的
• nonlinearity　非直线性
• cubic　三次方程
• algebraic　代数的
• epsilon　小的正数
• transform　变换
• perturbation　扰动
• continuation　继续
• differential　差动的