Geodesic
Analysis of the Avalos–Triggiani problem for the linear Oskolkov system of the highest order and a system of wave equations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 2, pp. 104-110 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Avalos–Triggiani problem for a system of wave equations and a linear Oskolkov system of the highest order is investigated. The mathematical model contains a linear Oskolkov system describing the flow of an incompressible viscoelastic Kelvin–Voigt fluid of of the highest order, and a wave vector equation corresponding to some structure immersed in the specified fluid. Based on the method proposed by the authors of this problem, the theorem of the existence of the unique solution to the Avalos–Triggiani problem for the indicated systems is proved.
Keywords: Avalos–Triggiani problem, incompressible viscoelastic fluid, linear Oskolkov systems. 
@article{VYURU_2024_17_2_a8,
     author = {T. G. Sukacheva and A. O. Kondiukov},
     title = {Analysis of the {Avalos{\textendash}Triggiani} problem for the linear {Oskolkov} system of the highest order and a system of wave equations},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {104--110},
     year = {2024},
     volume = {17},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2024_17_2_a8/}
}
TY  - JOUR
AU  - T. G. Sukacheva
AU  - A. O. Kondiukov
TI  - Analysis of the Avalos–Triggiani problem for the linear Oskolkov system of the highest order and a system of wave equations
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2024
SP  - 104
EP  - 110
VL  - 17
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VYURU_2024_17_2_a8/
LA  - en
ID  - VYURU_2024_17_2_a8
ER  - 
%0 Journal Article
%A T. G. Sukacheva
%A A. O. Kondiukov
%T Analysis of the Avalos–Triggiani problem for the linear Oskolkov system of the highest order and a system of wave equations
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2024
%P 104-110
%V 17
%N 2
%U http://geodesic.mathdoc.fr/item/VYURU_2024_17_2_a8/
%G en
%F VYURU_2024_17_2_a8
T. G. Sukacheva; A. O. Kondiukov. Analysis of the Avalos–Triggiani problem for the linear Oskolkov system of the highest order and a system of wave equations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 2, pp. 104-110. http://geodesic.mathdoc.fr/item/VYURU_2024_17_2_a8/

[1] Avalos G., Lasiecka I., Triggiani R., “Higher Regularity of a Coupled Parabolic-Hyperbolic Fluid-Structure Interactive System”, Georgian Mathematical Journal, 15:3 (2008), 403–437 | DOI | MR | Zbl

[2] Avalos G., Triggiani R., “Backward Uniqueness of the S.C. Semigroup Arising in Parabolic-Hyperbolic Fluid-Structure Interaction”, Differential Equations, 245:3 (2008), 737–761 | DOI | MR | Zbl

[3] Oskolkov A.P., “Initial-Boundary Value Problems for Equations of Motion of Kelvin–Voight Fluids and Oldroyd fluids”, Proceedings of the Steklov Institute of Mathematics, 179 (1989), 137–182 | MR | Zbl

[4] Sviridyuk G.A., Sukacheva T.G., “The Avalos–Triggiani Problem for the Linear Oskolkov System and a System of Wave Equations”, Computational Mathematics and Mathematical Physics, 62:3 (2022), 427–431 | DOI | DOI | MR | Zbl

[5] Sukacheva T.G., Sviridyuk G.A., “The Avalos–Triggiani Problem for the Linear Oskolkov System and a System of Wave Equaions. II”, Journal of Computational and Engineering Mathematics, 9:2 (2022), 67–72 | DOI | MR | Zbl

[6] Kondyukov A.O., Sukacheva T.G., “The Linear Oskolkov System of Nonzero Order in the Avalos–Triggiani Problem”, Journal of Computational and Engineering Mathematics, 10:4 (2023), 17–23 | DOI

[7] Sukacheva T.G., Kondyukov A.O., “Analysis of the Avalos–Triggiani Problem for the Linear Oskolkov System of Nonzero Order and a System of Wave Equations”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 16:4 (2023), 93–98 | DOI | Zbl

[8] Sukacheva T.G., “Unsteady Linearized Model of the Motion of an Incompressible High-Order Viscoelastic Fluid”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 17(150):3 (2009), 86–93 | Zbl

[9] Oskolkov A.P., “Some Nonstationary Linear and Quasilinear Systems Occurring in the Investigation of the Motion of Viscous Fluids”, Journal of Soviet Mathematics, 10 (1978), 299–335 | DOI | MR | Zbl

[10] Sviridyuk G.A., Sukacheva T.G., “Phase Spaces of a Class of Operator Semilinear Equations of Sobolev Type”, Differential Equations, 26:2 (1990), 188–195 | MR | Zbl

[11] Sviridyuk G.A., Sukacheva T.G., “On the Solvability of a Nonstationary Problem Describing the Dynamics of an Incompressible Viscoelastic Fluid”, Mathematical Notes, 63:3 (1998), 388–395 | DOI | DOI | MR | Zbl

[12] Kondyukov A.O., Sukacheva T.G., “Phase Space of the Initial–Boundary Value Problem for the Oskolkov System of Nonzero Order”, Computational Mathematics and Mathematical Physics, 55:5 (2015), 823–828 | DOI | DOI | MR | Zbl

[13] Vasyuchkova K.V., Manakova N.A., Sviridyuk G.A., “Some Mathematical Models with a Relatively Bounded Operator and Additive “White Noise””, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 10:4 (2017), 5–14 | DOI | Zbl

[14] Sviridyuk G.A., Zamyshlyaeva A.A., Zagrebina S.A., “Multipoint Initial-Final Value for one Class of Sobolev Type Models of Higher Order with Additive “White Noise””, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 11:3 (2018), 103–117 | DOI | Zbl

[15] Favini A., Zagrebina S.A., Sviridyuk G.A., “Multipoint Initial-Final Value Problems for Dinamical Sobolev-Type Equations in the Space of Noises”, Electronic Journal of Differential Equations, 2018:128 (2018), 1–10 | MR