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讲准字322号:Stability analysis in geometric optics and non-relativistic limit of Klein-Gorodon equations.

发布时间:2017-11-14|浏览次数:

题目:Stability analysis in geometric optics and non-relativistic limit of Klein-Gorodon equations.

主讲:吕勇

时间:2017年11月19日9:30-10:30

地点:理学院206报告厅

主办:理学院


主讲简介:吕勇,南京大学教授。研究专长:偏微分方程。吕勇,现为南京大学数学系副教授。2017年入选中组部第13批“青年千人计划”。吕勇本科毕业于中国科技大学数学系,在法国巴黎七大取得硕士和博士学位,之后在布拉格查理大学从事博士后研究。吕勇的主要研究领域是偏微分方程的数学分析,主要在非线性几何光学方程以及流体力学方程两个方向,取得了突出的成绩。主要研究成果发表在ARMA,Mémoires de la Société Mathématique de France,CVPDE, SIAM: Journal on Mathematical Analysis等很具影响力的期刊上。

主讲内容:The Klein-Gordon equation is a relativistic form of the Schrödinger equation. In the non-relativistic limit (as the speed of light goes to infinity) of Klein-Gordon equations, one derives, at least formally, Schrödinger equations. We find a strong connection between the stability analysis in geometric optics and non-relativistic limit of Klein-Gorodon equations. By employing the techniques in geometric optics, we obtain the optimal convergence rates. Moreover, for quadratic nonlinearities, we show the long time approximation of Klein-Gordon equations by Schrödinger equations in the non-relativistic limit regime. Even in the framework of geometric optics, we find that the strong transparency conditions are not satisfied. We introduce a compatible condition and a singular localization method which allows us to prove the stability of WKB solutions over long time intervals. This compatible condition is weaker than the strong transparency condition. The singular localization method allows us to do delicate analysis near resonances


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