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An existence result for the fractional Kelvin–Voigt’s model on time-dependent cracked domains
Journal of Evolution Equations ( IF 1.4 ) Pub Date : 2021-06-04 , DOI: 10.1007/s00028-021-00713-2 Maicol Caponi , Francesco Sapio
中文翻译:
分数阶 Kelvin-Voigt 模型在瞬态裂纹域上的存在性结果
更新日期:2021-06-04
Journal of Evolution Equations ( IF 1.4 ) Pub Date : 2021-06-04 , DOI: 10.1007/s00028-021-00713-2 Maicol Caponi , Francesco Sapio
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.
中文翻译:
分数阶 Kelvin-Voigt 模型在瞬态裂纹域上的存在性结果
我们证明了分数 Kelvin-Voigt 模型的存在性结果,该模型涉及时间相关裂纹域上的 Caputo 导数。我们首先展示了这个问题的正则化版本的解决方案的存在。然后,我们使用紧凑性论证推导出分数 Kelvin-Voigt 模型承认满足能量耗散不等式的解。最后,我们证明当裂纹不动时,解是唯一的。