报 告 人：Eric SERE 教授

工作单位：巴黎第九大学-巴黎文理联大(Paris IX Dauphine-Paris Sciences et Lettres)

报告时间：2019年11月7日下午16：30

报告地点：学院南阶梯教室

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 Gâteau 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.

报告人简介：

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。