THE LINEAR OSKOLKOV SYSTEM OF NON-ZERO ORDER IN THE AVALOS--TRIGGIANI PROBLEM

A. O. Kondyukov, T. G. Sukacheva

Abstract


The Avalos--Triggiani problem for a linear Oskolkov system of non-zero order and a system of wave equations is investigated. The mathematical model contains a linear Oskolkov system of non-zero order and a wave vector equation corresponding to some structure immersed in the Kelvin--Voight incompressible viscoelastic fluid.  The theorem of the existence of the unique solution to the Avalos--Triggiani problem for the indicated systems is proved using the method proposed by the authors of this problem. The results of this article generalize the results received earlier.

Keywords


Avalos--Triggiani problem; incompressible viscoelastic fluid; linear Oskolkov system.

Full Text:

PDF

References


Avalos G., Lasiecka I., Triggiani R. Higher Regularity of a Coupled Parabolic-Hyperbolic Fluid-Structure Interactive System. Georgian Mathematical Journal, 2008, vol. 15, no. 3, pp. 403–437. DOI: 10.1515/gmj.2008.403

Avalos G., Triggiani R. Backward Uniqueness of the S.C. Semigroup Arising in Parabolic-Hyperbolic Fluid-Structure Interaction. Differential Equations, 2008, vol. 245, pp. 737–761. DOI: 10.1016/j.jde.2007.10.036

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, 1989, vol. 179, pp. 137–182.

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, 2022, vol. 62, no. 3, pp. 427–431. DOI: 10.1134/s0965542522020105

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, 2022, vol. 9, no.2, pp. 67–72. DOI: 10.14529/jcem220206

Oskolkov A.P. Some Nonstationary Linear and Quasilinear Systems Occurring in the Investigation of the Motion of Viscous Fluids. Journal of Soviet Mathematics, 1978, vol. 10, pp. 299–335. (1978). DOI: 10.1007/BF01566608

Sviridyuk G.A., Sukacheva T.G. Phase Spaces of a Class of Operator Semilinear Equations of Sobolev Type. Differential Equations, 1990, vol. 26, no. 2, pp. 188–195.

Sviridyuk, G.A., Sukacheva, T.G. On the Solvability of a Nonstationary Problem Describing the Dynamics of an Incompressible Viscoelastic Fluid. Mathematical Notes, 1998, vol. 63, no. 3, pp. 388–395. DOI: 10.1007/BF02317787

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, 2015, vol. 55, no. 5, pp. 823–828 (2015). DOI: 10.1134/S0965542515050127

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, 2017, vol. 10, no. 4, pp. 5–14. DOI: 10.14529/mmp170401

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, 2018, vol. 11, no. 3, pp. 103–117. DOI: 10.14529/mmp180308

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, vol. 2018, article ID: 128.


Refbacks

  • There are currently no refbacks.


 Save