<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>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/25213649 |
| Date | 13 February 2024 |
| Creators | Gavin Ainsley Glenn (17958005) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Asymptotic_Analysis_of_Models_for_Geometric_Motions/25213649 |
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