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Convergence of discrete Aubry-Mather model in the continuous limit and related topics - 苏喜锋教授(北京师范大学)

作者:   来源:  时间:2018-06-12

题目:Convergence of discrete Aubry-Mather model in the continuous limit and related topics

报告人: 苏喜锋教授(北京师范大学)

Abstract:

We will consider the Frenkel-Kontorova models and their higher dimensional generalizations, Aubry-Mather model, and talk about the corresponding discrete weak KAM theory and the two approximate schemes. The discrete models can be thought of as the Hamilton-Jacobi equation on the crystals (one may possibly extend the results to the quasi-crystals case in some sense). The existence of the discrete weak KAM solutions is related to the additive eigenvalue problem in ergodic optimization. Moreover, we will show that the discrete weak KAM solutions from the approximate schemes converge to the weak KAM solutions of the autonomous Tonelli Hamilton-Jacobi equations as the time step goes to zero. In particular, one may possible use the results here to give another proof of the weak KAM theorem of A. Fathi. This is a joint work with Prof. Philippe Thieullen.

时间:6月12日(周二)上午9:00-10:00

地点:首都师大新教2楼  827  教室

 

 

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