Scientific seminar “Study of mathematical models of the motion of polymer solutions”

30 March at 12:00 MSK

Topic: Study of mathematical models of the motion of polymer solutions.

The report is devoted to the mathematical study of a number of initial-boundary value problems that describe the qualitative properties of models of the motion of viscoelastic media. In the first part of the report we study a mathematical model with a constitutive relationship that satisfies the principle of objectivity (that is, with a relationship that does not change under the Galilean change of variables). For this initial-boundary value problem, we prove the existence of weak solutions, the existence of an optimal feedback control, and the existence of trajectory, global, and pullback attractors. In the second part of the report, we study thermoviscoelastic models of non-Newtonian hydrodynamics (Voigt model, Kelvin-Voigt model, and a model with a constitutive relation satisfying the principle of objectivity) with viscosity depending on temperature.

For these initial-boundary value problems, we prove theexistence of weak solutions and the existence of an optimal feedback control are proved. The final part of the report is devoted to the alpha model (interest in which arose after J. Leray's works for the alpha model of the Navier-Stokes system) of the motion of viscoelastic media with a fractional derivative in the constitutive relation. For this initial-boundary value problem, we prove the existence of weak solutions. All these problems are studied on the basis of a relatively new approximation-topological method and its variants of the study of problems in hydrodynamics, developed in the Voronezh school of mathematics.

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