Sergey Glyzin
ul. Sovetskaya 14, Yaroslavl, 150003 Russia
Regional Scientific and Educational Mathematical Center of the Yaroslavl State University
Publications:
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Glyzin S. D., Kashchenko S. A., Kosterin D. S.
Abstract
Spatially distributed integro-differential systems of equations with periodic boundary conditions
are considered. In applications, such systems arise as limiting ones for some nonlinear
fully coupled ensembles. The simplest critical cases of zero and purely imaginary eigenvalues in
the problem of stability of the zero equilibrium state are considered.
In these two situations, quasinormal forms are constructed, for which the question of the
existence of piecewise constant solutions is studied. In the case of a simple zero root, the
conditions for the stability of these solutions are determined. The existence of piecewise constant
solutions with more than one discontinuity point is shown. An algorithm for calculating solutions
of the corresponding boundary value problem by numerical methods is presented. A numerical
experiment is performed, confirming the analytical constructions.
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