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1	Asymptotic Analysis of Models for Geometric Motions Gavin Ainsley Glenn (17958005) 13 February 2024 (has links) <p dir="ltr">In Chapter 1, we introduce geometric motions from the general perspective of gradient flows. Here we develop the basic framework in which to pose the two main results of this thesis.</p><p dir="ltr">In Chapter 2, we examine the pinch-off phenomenon for a tubular surface moving by surface diffusion. We prove the existence of a one parameter family of pinching profiles obeying a long wavelength approximation of the dynamics.</p><p dir="ltr">In Chapter 3, we study a diffusion-based numerical scheme for curve shortening flow. We prove that the scheme is one time-step consistent.</p> Numerical analysis Partial differential equations partial differential equations (PDE) motion by mean curvature Mean Curvature Flow surface diffusion models gradient flows diffusion generated motion codimension-2 pinch-off dynamics consistency estimates heat equation axisymmetric surface diffusion Geometric PDEs one-parameter family singularity formation Numerical analysis. convergence rate Differential equations. Ordinary Differential Equations (ODE)