Computational & Applied Mathematics (CAM) Seminar

Time: 3:15pm, Wednesday, Dec. 21 (特别时间：周三下午 3:15)

Location: Conference Room 4, Jin Chun Yuan West Bldg.

(近春园西楼二楼第四会议室)

Title: Stability analysis in geometric optics and non-relativistic limit of Klein-Gordon equations

Speaker: Yong LU, (吕勇，南开大学陈省身数学研究所)

Abstract: 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. This talk is based on joint-works with Prof. Zhifei Zhang.

For details, please see http://ymsc.tsinghua.edu.cn/CAM/