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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.15984 |
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| _version_ | 1866917761775566848 |
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| author | Collins, Carson Feldman, William M |
| author_facet | Collins, Carson Feldman, William M |
| contents | We study the uniqueness and regularity of minimizing movements solutions of a droplet model in the case of piecewise monotone forcing. We show that such solutions evolve uniquely on each interval of monotonicity, but branching non-uniqueness may occur where jumps and monotonicity changes coincide. This classification of minimizing movements solutions allows us to reduce the quasi-static evolution to a finite sequence of elliptic problems and establish $L^\infty_tC^{1,1/2-}_x$-regularity of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimizing movements solutions for a monotone model of droplet motion Collins, Carson Feldman, William M Analysis of PDEs We study the uniqueness and regularity of minimizing movements solutions of a droplet model in the case of piecewise monotone forcing. We show that such solutions evolve uniquely on each interval of monotonicity, but branching non-uniqueness may occur where jumps and monotonicity changes coincide. This classification of minimizing movements solutions allows us to reduce the quasi-static evolution to a finite sequence of elliptic problems and establish $L^\infty_tC^{1,1/2-}_x$-regularity of solutions. |
| title | Minimizing movements solutions for a monotone model of droplet motion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.15984 |