Blar i forfatter "Lychagin, Valentin"

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    • Continuum mechanics of media with inner structures 

      Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey (Journal article; Tidsskriftartikkel; Peer reviewed, 2020-11-05)
      We propose a geometrical approach to the mechanics of continuous media equipped with inner structures and give the basic (Navier–Stokes, mass conservation and energy conservation) equations of their motion.

    • Finite dimensional dynamics for nonlinear filtration equation 

      Akhmetzyanov, Atlas V.; Kushner, Alexei G.; Lychagin, Valentin (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-09-01)
      We construct new finite dimensional submanifolds in the solution space of nonlinear differential filtration equations and describe the corresponding evolutionary dynamics. This method is implemented in a computer program of symbolic computations Maple.

    • On structure of linear differential operators, acting on line bundles 

      Lychagin, Valentin; Yumaguzhin, Valeriy (Journal article; Tidsskriftartikkel; Peer reviewed, 2019-11-14)
      We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting on line bundles over smooth manifolds with respect to groups of automorphisms.

    • Real gas flows issued from a source 

      Lychagin, Valentin; Roop, Mikhail (Journal article; Tidsskriftartikkel; Peer reviewed, 2019-12-23)
      Stationary adiabatic flows of real gases issued from a source of given intensity are studied. Thermodynamic states of gases are described by Legendrian or Lagrangian manifolds. Solutions of Euler equations are given implicitly for any equation of state and the behavior of solutions of the Navier–Stokes equations with the viscosity considered as a small parameter is discussed. For different intensities ...

    • Symmetries and Differential Invariants for Inviscid Flows on a Curve 

      Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey (Journal article; Tidsskriftartikkel; Peer reviewed, 2021-02-04)
      Symmetries and the corresponding fields of differential invariants of the inviscid flows on a curve are given. Their dependence on thermodynamic states of media is studied, and a classification of thermodynamic states is given.

    • Symmetry classification of viscid flows on space curves 

      Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey (Journal article; Tidsskriftartikkel; Peer reviewed, 2020-11-01)
      Symmetries and differential invariants of viscid flows with viscosity depending on temperature on a space curve are given. Their dependence on thermodynamic states of media is studied, and a classification of thermodynamic states is given.