Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity
作者: Alberto LastraStephane 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 expansionBorel-Laplace transformFourier transformCauchy problemFormal power seriesNonlinear integro-differential equationNonlinear partial differential equationSingular 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.
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  • 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