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Birkhoff normal form for some nonlinear PDEs with inner parameter
澳门新葡8455最新网站:2016年11月23日 09:35 点击数:

报告人:丛洪滋

报告地点:澳门新葡8455最新网站317室

报告澳门新葡8455最新网站:2016年11月25日星期五15:00-16:00

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报告摘要:

In this talk, we are concerned the long time stability of the origin for infinite dimensional Hamiltonian systems generated by some nonlinear partial differential equations (PDEs) with inner parameter. We prove, under some nonresonant conditions which are fulfilled for most initial data, that for any integer $M\geq 3$ there exists a canonical transformation that puts the Hamiltonian into a partial Birkhoff normal form up to a reminder of order $M+1$. As a dynamical consequence, the long time stability of the origin is obtained. Finally, we take 1-dimensional nonlinear Schr$\ddot{\mbox{o}}$dinger equation with Dirichlet boundary conditions as a model problem. The technique of proof is applicable to quite general semilinear equation in one space dimension.

主讲人概况:

丛洪滋,大连理工大学数学科学新葡京最新官网副教授。2009年6月获复旦大学理学博士学位。从事无穷维哈密顿系统KAM理论和Birkhoff normal form理论的研究工作,在Memoirs AMS,JDE等期刊共发表论文8篇。

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