Weak solvability and convergence of solutions for the fractional Voigt-
	    
	    
	   model of a viscoelastic medium

Zvyagin, A. V.

doi:10.1070/rm9880

Cited by 16 publications

(7 citation statements)

References 7 publications

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“…For a number of non‐Newtonian systems, similar results were obtained in Orlov and Sobolevskii 7 and Orlov 8 . Let us note that fractional analogues of Newton, Maxwell, Kelvin–Voigt, Jeffrey, Oldroyd, Zener, anti‐Zener, and Burgers models are widely known and used (see, e.g., Gorenflo & Mainardi, 1 Bagleys & Torvik, 2 Caputo & Mainardi, 3,4 Mainardi & Spada, 9 Scott‐Blair, 10 Zvyagin, 11 and references therein).…”

Section: Introductionsupporting

confidence: 63%

On strong solutions of fractional nonlinear viscoelastic model of Voigt type

Zvyagin

Orlov

2020

Math Methods in App Sciences

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Section: Introductionsupporting

confidence: 63%

On strong solutions of fractional nonlinear viscoelastic model of Voigt type

Zvyagin

Orlov

2020

Math Methods in App Sciences

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“…Note that a special case of this initial boundary value problem under consideration, based on the solvability proved in this paper, was announced in [36]. The purpose of this paper is to establish the existence of weak solutions to the initial boundary value problem ( 19)- (22). For this purpose, we use the topological approximation approach to the study of mathematical hydrodynamics problems.…”

Section: Introductionmentioning

confidence: 95%

“…and initial condition v(0) = v 0 is a weak solution to problem (19)- (22). Here, z is the RLF associated with v.…”

Section: Preliminariesmentioning

confidence: 99%

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Investigation of the Weak Solvability of One Viscoelastic Fractional Voigt Model

Zvyagin,

Kostenko

2023

Mathematics

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This article is devoted to the investigation of the weak solvability to the initial boundary value problem, which describes the viscoelastic fluid motion with memory. The memory of the fluid is considered not at a constant position of the fluid particle (as in most papers on this topic), but along the trajectory of the fluid particle (which is more physical). This leads to the appearance of an unknown function z, which is the trajectory of fluid particles and is determined by the velocity v of a fluid particle. However, in this case, the velocity v belongs to L2(0,T;V1), which does not allow the use of the classical Cauchy Problem solution. Therefore, we use the theory of regular Lagrangian flows to correctly determine the trajectory of the particle. This paper establishes the existence of weak solutions to the considered problem. For this purpose, the topological approximation approach to the study of mathematical hydrodynamics problems, constructed by Prof. V. G. Zvyagin, is used.

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“…However, most of the works on the solvability of alpha-models are devoted to models of the motion of an ideal or Newtonian fluid [11][12][13][14]. Only in the last few years, works began to appear on the study of alpha-models of non-Newtonian fluid [15][16][17][18]. This work continues the study of alpha-models for non-Newtonian fluids, namely, for the fractional Voigt model of the viscoelastic medium [19].…”

Section: Introductionmentioning

confidence: 99%

Optimal Feedback Control Problem for the Fractional Voigt-α Model

Zvyagin

Ustiuzhaninova

2020

Mathematics

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The study of the existence of an optimal feedback control problem for the initial-boundary value problem that describes the motion of the fractional Voigt- α model of a viscoelastic medium is investigated in this paper. In this model, the Voigt rheological relation is considered with the left-side fractional Riemann-Liouville derivative, which allows to take into account the memory of the medium. Also in this model, the memory is considered along the trajectory of the motion of fluid particles, determined by the velocity field. Due to the insufficient smoothness of the velocity field and, as a consequence, the impossibility of uniquely determining the trajectory for the velocity field for any initial value, a weak solution to the problem under study is introduced using regular Lagrangian flows. Based on the approximation-topological approach to the study of fluid dynamic problems, the existence of an optimal solution that gives a minimum to a given cost functional is proved.

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Weak solvability and convergence of solutions for the fractional Voigt- model of a viscoelastic medium

Cited by 16 publications

References 7 publications

On strong solutions of fractional nonlinear viscoelastic model of Voigt type

On strong solutions of fractional nonlinear viscoelastic model of Voigt type

Investigation of the Weak Solvability of One Viscoelastic Fractional Voigt Model

Optimal Feedback Control Problem for the Fractional Voigt-α Model

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