Lagrange and Lyapunov stability of degenerate differential equations

On Friday December 1, 2023 our postdoctoral researcher Dr. Maria Filipkovska will talk on “Lagrange and Lyapunov stability of degenerate differential equations” at the Dynamical systems and control seminar organized at Julius-Maximilians-Universität Würzburg.

Abstract. The development of modern technologies leads to the appearance of various types of nonlinear mathematical models describing complex technical (mechanical, electrical, gas) and socio-economic (logistics, marketing) systems. Depending on the model, it is necessary to apply different methods for studying the existence and stability of its solutions.

In this talk, for degenerate differential equations, conditions of the Lagrange stability and instability, the Lyapunov stability and instability, and asymptotic stability (including conditions of asymptotic stability in the large or complete stability) will be presented.

The Lagrange stability of a differential equation guarantees its global solvability for all consistent initial values and the boundedness of all its solutions. The Lagrange instability enables to identify solutions with finite escape time, i.e. the solutions blowing up in finite time. The definitions of the Lyapunov stability and instability for degenerate differential equations are similar to the corresponding definitions for explicit ordinary differential equations. Note that the Lyapunov stability (respectively, instability) of a solution, in general, does not imply its Lagrange stability (respectively, instability). The Lagrange stability of a solution, in general, also does not imply its Lyapunov stability, but the Lagrange instability of the solution implies its Lyapunov instability.

Degenerate differential equations describe various dynamical systems which are nonlinear and may have nonlinear algebraic (functional) relationships between the coordinates of variables and relationships between these variables and external influences. The results presented in this talk allow one to analyze stability (in different senses) of such dynamical systems.

Fri. December 1, 2023 at 14:15H (local time)

Room 01.003. Julius-Maximilians-Universität Würzburg
Emil-Fischer-Strasse 40, 97074 Würzburg