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Eric SERE:Ekeland’s variational principle and the Nash-Moser theore:(时间11.7)
【 澳门威斯尼人平台登陆:  校对时间:2019年11月07日 08:59  访问次数: 】

报 告 人:Eric SERE 教授巴黎第九大学-巴黎文理联大

报告时间:20191171630

报告地点:学院南阶梯教室

主办单位:数学与统计学院

欢迎光临!

报告摘要:This is joint work with Ivar Ekeland. The Nash-Moser theorem allows to solve a functional equation F(u)=0 in a "scale" of Banach spaces, assuming that F(0) is very small and that near 0 the differential DF has a right inverse losing derivatives. The classical proof uses a Newton iteration scheme, which converges when F is of class C^2. In contrast, we only assume that F is continuous and has a G?teau first differential, which is right-invertible with loss of derivatives. In our iteration scheme, each step consists in solving a Galerkin approximation of the equation, using Ekeland's variational principle. We apply our method to a singular perturbation problem with loss of derivatives studied by Texier-Zumbrun. We compare the two results and we show that ours improves significantly on theirs, when applied, in particular, to a nonlinear Schrodinger Cauchy problem with highly oscillatory initial data: we are able to deal with larger oscillations.

Eric SERE教授是活跃在非线性分析领域的法国数学家,目前任职于巴黎第九大学决策数学研究所(CEREMADE)。其主要研究方向为变分法及其Hamiltonian系统和量子力学中的应用。



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