An existence result for the fractional Kelvin-Voigt's model on time-dependent cracked domains
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866908573845422080 |
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| author | Caponi, Maicol Sapio, Francesco |
| author_facet | Caponi, Maicol Sapio, Francesco |
| contents | We prove an existence result for the fractional Kelvin-Voigt's model involving Caputo's derivative on time-dependent cracked domains. We first show the existence of a solution to a regularized version of this problem. Then, we use a compactness argument to derive that the fractional Kelvin-Voigt's model admits a solution which satisfies an energy-dissipation inequality. Finally, we prove that when the crack is not moving, the solution is unique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_02214 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | An existence result for the fractional Kelvin-Voigt's model on time-dependent cracked domains Caponi, Maicol Sapio, Francesco Analysis of PDEs 35L53, 35R11, 35A01, 35Q74, 74H20, 74R10 We prove an existence result for the fractional Kelvin-Voigt's model involving Caputo's derivative on time-dependent cracked domains. We first show the existence of a solution to a regularized version of this problem. Then, we use a compactness argument to derive that the fractional Kelvin-Voigt's model admits a solution which satisfies an energy-dissipation inequality. Finally, we prove that when the crack is not moving, the solution is unique. |
| title | An existence result for the fractional Kelvin-Voigt's model on time-dependent cracked domains |
| topic | Analysis of PDEs 35L53, 35R11, 35A01, 35Q74, 74H20, 74R10 |
| url | https://arxiv.org/abs/2011.02214 |