A Family of Piecewise-Smooth Solutions of a Class of Spatially Distributed Equations

被引：0

作者：

S. A. Kaschenko ^{[1
]}

D. S. Kosterin ^{[1
]}

S. D. Glyzin ^{[1
]}

机构：

[1] P. G. Demidov Yaroslavl State University, Yaroslavl

来源：

Journal of Mathematical Sciences | 2024年 / 285卷 / 3期

关键词：

cluster synchronization; evolutionary spatially distributed equations; piecewise constant solutions; stability;

D O I：

10.1007/s10958-024-07447-9

中图分类号：

学科分类号：

摘要：

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 the boundary-value problem by numerical methods is presented. A numerical analysis of the dynamics of the boundary-value problem is performed. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

引用

页码：352 / 363

页数：11

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