Abstract
The existence of partial solutions, increasing with time, of the linearized equations of a nonisothermal incompressible polymer liquid is established.
Similar content being viewed by others
References
Yu. A. Altukhov, A. S. Gusev, and G. V. Pyshnograi, Introduction to the Mesoscopic Theory of Fluid Polymer Systems (AltGPA, Barnaul, 2012).
A. M. Blokhin and A. Yu. Goldin, “On linear stability of an incompressible polymer liquid at rest,” Sib. Zh. Chist. Prikl. Mat. 16 (4), 17–27 (2016).
A. N. Mordvinov and B. L. Smorodin, “Electroconvection under injection from cathode and heating from above,” J. Exp. Theor. Phys. 114 (5), 870–877 (2012).
A. M. Blokhin and A. S. Rudometova, “Stationary solutions to the equations describing the nonisothermal electrical convection of a weakly conductive incompressible polymeric fluid,” Sib. Zh. Ind. Mat. 18 (1), 3–13 (2015).
S. K. Godunov, Ordinary Differential Equations with Constant Coefficients (Novosibirsk. Gos. Univ., Novosibirsk, 1994), Vol. 1 [in Russian].
N. N. Yanenko, The Method of Fractional Steps: The Solution of Problems of Mathematical Physics in Several Variables (Nauka, Novosibirsk, 1967; Springer-Verlag, Berlin, 1971).
M. A. Lavren’tev and B. V. Shabat, Methods of the Theory of Functions of Complex Variable (Nauka, Moscow, 1973) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.M. Blokhin, R.E. Semenko, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 11, pp. 1831–1843.
Rights and permissions
About this article
Cite this article
Blokhin, A.M., Semenko, R.E. Linear instability of the state of rest for an incompressible polymer liquid upon injection from the cathode and heating from the top. Comput. Math. and Math. Phys. 57, 1796–1807 (2017). https://doi.org/10.1134/S0965542517110045
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542517110045