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This article is cited in 11 scientific papers (total in 11 papers)
Investigation of the weak solubility of the fractional Voigt alpha-model
A. V. Zvyaginab a Voronezh State Pedagogical University
b Voronezh State University
Abstract:
This paper is devoted to investigating the weak solubility of the alpha-model for a fractional viscoelastic Voigt medium.
The model involves the Voigt rheological relation with a left Riemann–Liouville fractional derivative, which
accounts for the medium's memory. The memory is considered along the trajectories of fluid particles
determined by the velocity field. Since the velocity field is not smooth enough to uniquely determine the trajectories
for every initial value, we introduce weak solutions of this problem using regular Lagrangian flows. On the basis of
the approximation-topological approach to the study of hydrodynamical problems, we prove the existence of weak
solutions of the alpha-model and establish the convergence of solutions of the alpha-model to solutions of
the original model as the parameter $\alpha$ tends to zero.
Keywords:
existence theorem, weak solubility, Voigt model, alpha-model, fractional derivative.
Received: 11.02.2020
Citation:
A. V. Zvyagin, “Investigation of the weak solubility of the fractional Voigt alpha-model”, Izv. RAN. Ser. Mat., 85:1 (2021), 66–97; Izv. Math., 85:1 (2021), 61–91
Linking options:
https://www.mathnet.ru/eng/im9020https://doi.org/10.1070/IM9020 https://www.mathnet.ru/eng/im/v85/i1/p66
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Abstract page: | 458 | Russian version PDF: | 90 | English version PDF: | 43 | Russian version HTML: | 155 | References: | 45 | First page: | 26 |
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