The instability of the solutions of the generalized Sobolev type equation on a graph

Abstract

This article is devoted to computational experiments on the basis of the Galerkin method. Its purpose is to illustrate the instability of the trivial solution of Hoff equations defined on a finite connected oriented graph. The vertices of set conditions for continuity and balance flows are provided. This equation models describe dynamics of buckling a double-tee girder under constant load and belong to a large class of the Sobolev type semilinear equations. This paper describes an algorithm and considers an example of the work program developed in the system of Maple computer mathematics. We use the second Lyapunov's method adapted to the case of incomplete normed spaces to describe the stability.