Qualitative properties of solutions of one class of evolutionary systems

Authors

  • A. I. Shevchenko
  • A. S. Minenko

DOI:

https://doi.org/10.15407/dopovidi2015.01.036

Keywords:

approximation, Bean model, superconductivity

Abstract

The nonlinear nonstationary systems used as approximations to the well-known Bean model in the theory of type-II superconductivity in the 3D case are studied. An analogous system with convection term playing the role of damping is considered as well. These systems are closely related to the system of equations for a porous medium. The finiteness of the carrier of a solution of the Cauchy problem for nonlinear nonstationary systems in the 3D case is established.

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References

Yin H. M. Quarterly of Appl. Math. 2001, 59, No 1: 47–66.

Yin H. M., Li B. Q., Zon J. Discrete and Continuous Dynamical Systems, 2002, 8, No 3: 781–794. https://doi.org/10.3934/dcds.2002.8.781

Kalashnikov A. S. Usp. mat. nauk, 1987, 42, No 2: 135–176 (in Russian).

Di Benedetto E. Degenerate parabolic equations, Berlin: Springer, 1993. https://doi.org/10.1007/978-1-4612-0895-2

Antontsev S. N., Dias J. I., Shmarev S. I. In: Applications to nonlinear PDEs and fluid mechanics, Boston: Birkhauser, 2002.

Barenblatt H. I. Prikl. matem. mekh., 1952, 16, No 1: 67–78 (in Russian).

Degtiarev S. P., Sanikidze T. A., Tedeev A. F. Reports of the National Academy of Sciences of Ukraine, 2007, No 3: 7–13 (in Russian).

Minenko A. S. Materialy nauchnogo seminara po teorii optimalnykh protsesov. Nauchnyi sovet po kibernetike AN UkrSSR, Kiev: In-t kibernetiki AN UkrSSRР, 1973, Vol. 1: 3–14.

Published

08.01.2025

How to Cite

Shevchenko, A. I., & Minenko, A. S. (2025). Qualitative properties of solutions of one class of evolutionary systems . Reports of the National Academy of Sciences of Ukraine, (1), 36–40. https://doi.org/10.15407/dopovidi2015.01.036

Issue

Section

Information Science and Cybernetics