Method of Lyapunov functionals construction in stability of delay evolution equations

By Tomás Caraballo, José Real, Leonid E. Shaikhet. 2007

69 citations recorded by the source corpus.

The investigation of stability for hereditary systems is often related to the construction of Lyapunov functionals. The general method of Lyapunov functionals construction which was proposed by V. Kolmanovskii and L. Shaikhet and successfully used already for functional differential equations, for difference equations with discrete time, for difference equations with continuous time, is used here to investigate the stability of delay evolution equations, in particular, partial differential equations.

Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/fb8206d9c04e885f2112ae519f37aa8ee3c31263

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In Applied Mathematics

In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions (2015, methodology): “As a consequence of some general results proved in [14], we will establish here some stability results for our model in the case of variable delay.”
General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback (2012, background): “Recently, the stability of PDEs with time-varying delays was studied in [5, 11, 23, 24, 25].”
Stability results for 2D Navier–Stokes equations with unbounded delay (2018, methodology): “The analysis of the Navier-Stokes equations with hereditary terms was initiated by Caraballo and Real in [14], and developed in [11, 12, 13, 7, 15, 8, 9, 10, 5, 6], where several issues have been investigated: the existence and uniqueness of solution, stationary solution, the existence of attractors”