Stability of a Stationary Solution to Non-Autonomous Linearized Hoff Model on a Geometrical Graph

The article is devoted to the study of the stability of a stationary solution for a non-autonomous linearized Hoff model on a geometric graph. This model makes it possible to describe a structure made of I-beams that is under external pressure and high temperatures. Using the stability conditions of a stationary solution for such a model, it is possible to describe the stability conditions of the structure described by this model on a geometric graph. Note that for the linearized Hoff model, the exponential dichotomy method cannot be applied, since the relative spectrum of the operator equation may intersect with the imaginary axis. Therefore, we use the second Lyapunov method to study of the stability. In addition to the introduction and the list of references, the article contains two parts. In the first of them, the conditions for the solvability of a non-autonomous linearized Hoff model on a geometric graph are given, and in the second, the stability of the stationary solution of this model is investigated.

Keywords

Sobolev type equations; relatively bounded operator; Lyapunov stability; local flow of operators; asymptotic stability.

References

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