Geodesic
A family of piecewise-smooth solutions of a class of spatially distributed equations
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 2, pp. 263-275.

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In this paper, we consider a spatially distributed equation with a periodic boundary condition and the zero integral mean condition in the spatial variable. The boundary-value problem under consideration has a family of solutions that are piecewise constant with respect to the spatial variable and have one discontinuity point. Conditions for the stability of such solutions are determined. The existence of piecewise constant solutions with more than one discontinuity point is shown. An algorithm for calculating solutions to a boundary-value problem by numerical methods is presented. A numerical analysis of the dynamics of the boundary-value problem is performed.
Keywords: evolutionary spatially distributed equations, stability, cluster synchronization.
Mots-clés : piecewise constant solutions 
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S. A. Kaschenko; D. S. Kosterin; S. D. Glyzin. A family of piecewise-smooth solutions of a class of spatially distributed equations. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 2, pp. 263-275. http://geodesic.mathdoc.fr/item/CMFD_2023_69_2_a5/

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