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Properties of the effective Hamiltonian and homogenization of the Hamilton-Jacobi equation

PDE Seminar
April 9, 2024
11:30 am - 12:20 pm
MW 154

Speaker:  Son Tu (Michigan State University)

Title: Properties of the effective Hamiltonian and homogenization of the Hamilton-Jacobi equation

Abstract: The homogenization of Hamilton-Jacobi equations in the periodic setting was pioneered by Lions, Papanicolaou, and Varadhan in the 1980s. However, understanding the intricate properties of the effective Hamiltonian and its impact on the homogenization limit across various settings remains a substantial open problem. In this presentation, we will discuss recent developments that highlight a connection between this phenomenon and weak KAM theory on a qualitative level, as well as present some quantitative results.

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Seminar - PDE