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Singular Limits of Evolutionary PDEs

Zu Chongzhi Distinguished Lecture ——Math-Physics Series

August 6, 2020 9:00 – 10:30 am, US Eastern time; 9:00 – 10:30 pm, China time

 

Singular Limits of Evolutionary PDEs

Qiangchang Ju, Institute of Applied Physics and Computational Mathematics

Abstract: Singular limits of a class of evolutionary systems of partial differential equations having two small parameters are considered. The two small parameters tend to zero at different rates and hence we have three time scales in systems.  Under appropriate conditions solutions are shown to exist and remain uniformly bounded for a fixed time as the two parameters tend to zero at different rates. Under further conditions the solutions of the original system tend to solutions of a limit equation as the parameters tend to zero. Finally , we apply the theory to the problem that motivated this research, namely the simultaneous zero Alfven number and zero Mach number limit of the scaled compressible inviscid MHD equations. The results develop the classical theory of singular limits for evolutionary partial differential equations by Klainerman and Majda, and Schochet in 1980s.

This is a joint research work with Bin Cheng from Surrey university and Steve Schochet from Tel-Aviv University.

 

Slides for the talk (click)

Recorded video for the talk (click)

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