In this thesis, we describe three contributions made to three different fields. First, we prove local stability of solutions to a 1D model equation of the 3D Euler equations. Second, we describe a model of human crowds where people are modeled by ellipses. Finally, we prove local stability of solutions for a family of convex programs.
University of Minnesota Ph.D. dissertation. April 2020. Major: Mathematics. Advisor: Vladimir Sverak. 1 computer file (PDF); vi, 98 pages.
A 1D Fluid Model On The Circle, An Algorithm For Simulating Dense Crowds, And Stability For Programs With Seminorm Objective And Linear Constraints.
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