On Solvability of an Initial-Boundary Value Problem for a Viscoelasticity Model with Fractional Derivatives

被引：8

作者：

Zvyagin, V. G. ^{[1
]}

Orlov, V. P. ^{[1
]}

机构：

[1] Voronezh State Univ, Res Inst Math, Voronezh, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2018年 / 59卷 / 06期

关键词：

viscoelastic medium; equation of motion; initial-boundary value problem; weak solution; anti-Zener model; fractional derivative; WEAK SOLVABILITY;

D O I：

10.1134/S0037446618060101

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the existence and uniqueness (the latter only in the plane case) of a weak solution to an initial-boundary value problem for the system of the equations of motion of a viscoelastic fluid, namely, for the anti-Zener model whose constitutive law contains fractional derivatives. We use the approximation of this problem by a sequence of regularized Navier-Stokes systems and passage to the limit.

引用

页码：1073 / 1089

页数：17

共 50 条

[31] Initial-boundary value problem for the Davey-Stewartson systems
Yang, L
Guo, BL
PROGRESS IN NATURAL SCIENCE, 1997, 7 (03) : 272 - 279
[32] Initial-boundary value problem for isothermal viscous gas equations
W. Weigant
P. I. Plotnikov
Doklady Mathematics, 2014, 89 : 135 - 138
[33] Initial-boundary value problem for the Davey-Stewartson systems
杨灵娥
郭柏灵
ProgressinNaturalScience, 1997, (03) : 18 - 25
[34] INITIAL-BOUNDARY VALUE PROBLEM FOR EULER EQUATIONS WITH INCOMPATIBLE DATA
Li, Dening
QUARTERLY OF APPLIED MATHEMATICS, 2018, 76 (01) : 47 - 64
[35] Initial-boundary Value Problems for Fractional Diffusion Equations with Time-Dependent Coefficients
Adam Kubica
Masahiro Yamamoto
Fractional Calculus and Applied Analysis, 2018, 21 : 276 - 311
[36] INITIAL-BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFUSION EQUATIONS WITH TIME-DEPENDENT COEFFICIENTS
Kubica, Adam
Yamamoto, Masahiro
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (02) : 276 - 311
[37] Initial-boundary Value Problem for a Time-fractional Subdiffusion Equation with an Arbitrary Elliptic Differential Operator
R. R. Ashurov
O. T Muhiddinova
Lobachevskii Journal of Mathematics, 2021, 42 : 517 - 525
[38] Initial-boundary value problem for a difference-differential diffusion equation with fractional derivative and distributed delay
P. S. Aleshin
A. N. Zarubin
Differential Equations, 2007, 43 : 1396 - 1402
[39] Initial-boundary Value Problem for a Time-fractional Subdiffusion Equation with an Arbitrary Elliptic Differential Operator
Ashurov, R. R.
Muhiddinova, O. T.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2021, 42 (03) : 517 - 525
[40] RELAXATION APPROXIMATION OF THE KERR MODEL FOR THE THREE-DIMENSIONAL INITIAL-BOUNDARY VALUE PROBLEM
Carbou, Gilles
Hanouzet, Bernard
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2009, 6 (03) : 577 - 614

← 1 2 3 4 5 →