Stability of multiphase mean curvature flow beyond circular topology changes
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916191449120768 |
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| author | Fischer, Julian Hensel, Sebastian Marveggio, Alice Moser, Maximilian |
| author_facet | Fischer, Julian Hensel, Sebastian Marveggio, Alice Moser, Maximilian |
| contents | We prove a weak-strong uniqueness principle for varifold-BV solutions to planar multiphase mean curvature flow beyond a circular topology change: Assuming that there exists a classical solution with an interface that becomes increasingly circular and shrinks to a point, any varifold-BV solution with the same initial interface must coincide with it, and any varifold-BV solution with similar initial data must undergo the same type of topology change. Our result illustrates the robustness of the relative energy method for establishing weak-strong uniqueness principles for interface evolution equations, showing that it may also be applied beyond certain topological changes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of multiphase mean curvature flow beyond circular topology changes Fischer, Julian Hensel, Sebastian Marveggio, Alice Moser, Maximilian Analysis of PDEs We prove a weak-strong uniqueness principle for varifold-BV solutions to planar multiphase mean curvature flow beyond a circular topology change: Assuming that there exists a classical solution with an interface that becomes increasingly circular and shrinks to a point, any varifold-BV solution with the same initial interface must coincide with it, and any varifold-BV solution with similar initial data must undergo the same type of topology change. Our result illustrates the robustness of the relative energy method for establishing weak-strong uniqueness principles for interface evolution equations, showing that it may also be applied beyond certain topological changes. |
| title | Stability of multiphase mean curvature flow beyond circular topology changes |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.02884 |