<p dir="ltr">We investigate the surface diffusion flow of smooth curves with anisotropic surface energy.</p><p dir="ltr">This geometric flow is the H−1-gradient flow of an energy functional. It preserves the area</p><p dir="ltr">enclosed by the evolving curve while at the same time decreases its energy. We show the</p><p dir="ltr">existence of a unique local in time solution for the flow but also the existence of a global in</p><p dir="ltr">time solution if the initial curve is close to the Wulff shape. In addition, we prove that the</p><p dir="ltr">global solution converges to the Wulff shape as t → ∞. In the current setting, the anisotropy</p><p dir="ltr">is not too strong so that the Wulff shape is given by a smooth curve. In the last section, we</p><p dir="ltr">formulate the corresponding problem when the Wulff shape exhibits corners.</p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/24759069 |
| Date | 09 December 2023 |
| Creators | Hanan Ussif Gadi (17592987) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/LONG_TIME_BEHAVIOR_OF_SURFACE_DIFFUSION_OFANISOTROPIC_SURFACE_ENERGY/24759069 |
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