Method of Lyapunov functionals construction in stability of delay evolution equations

DOI10.1016/j.jmaa.2007.01.038zbMath1178.34087OpenAlexW2032268770MaRDI QIDQ996897

Leonid Shaikhet, José Real, Tomás Caraballo Garrido

Publication date: 19 July 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://idus.us.es/xmlui/handle/11441/23678

zbMATH Keywords

stabilityevolution equationspartial differential equations2D Navier-Stokes model with delaysmethod of Lyapunov functionals construction

Mathematics Subject Classification ID

Partial functional-differential equations (35R10) Functional-differential equations in abstract spaces (34K30) Stability theory of functional-differential equations (34K20)

Related Items (37)

High order stable Runge-Kutta methods for nonlinear generalized pantograph equations on the geometric mesh ⋮ Exponential decay of solution to the viscoelastic porous-thermoelastic system of type III with boundary time-varying delay ⋮ Stability of an interconnected Schrödinger-heat system in a torus region ⋮ Asymptotic behavior of second sound thermoelasticity with internal time-varying delay ⋮ Stability of fractionally dissipative 2D quasi-geostrophic equation with infinite delay ⋮ Decay rates for delayed abstract thermoelastic systems with Cattaneo law ⋮ Well-posedness and exponential decay for a porous thermoelastic system with second sound and a time-varying delay term in the internal feedback ⋮ The exponential stability region of Timoshenko beam with interior delays and boundary damping ⋮ A NEW LaSalle-TYPE THEOREM FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS OF NEUTRAL TYPE ⋮ Uniform decay for thermoelastic diffusion problem of type III with delays ⋮ Backward stability and divided invariance of an attractor for the delayed Navier-Stokes equation ⋮ Dynamical level set method for parameter identification of nonlinear parabolic distributed parameter systems ⋮ Feedback stabilisation of an Euler–Bernoulli beam with the boundary time-delay disturbance ⋮ Boundary stabilization of a nonlinear viscoelastic equation with interior time-varying delay and nonlinear dissipative boundary feedback ⋮ Stability of delay evolution equations with stochastic perturbations ⋮ Some remarks on an environmental defensive expenditures model ⋮ Observations on evolutionary models with (or without) time lag, and on problematical paradigms ⋮ Unnamed Item ⋮ Uniform stability of second sound thermoelasticity with distributed delay ⋮ General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback ⋮ On the decay of a nonlinear wave equation with delay ⋮ Exponential dichotomies of evolution operators in Banach spaces ⋮ Exponential stability of an incompressible non-Newtonian fluid with delay ⋮ Uniform stability for thermoelastic systems with boundary time-varying delay ⋮ Stability analysis of heat flow with boundary time-varying delay effect ⋮ Stability results for 2D Navier-Stokes equations with unbounded delay ⋮ Unnamed Item ⋮ Stability of a stochastic model for HIV-1 dynamics within a host ⋮ Stability and stabilization for the three-dimensional Navier-Stokes-Voigt equations with unbounded variable delay ⋮ Stabilization of an Euler-Bernoulli beam with distributed damping under time delays in the boundary ⋮ Analysis of a stochastic \(2D\)-Navier-Stokes model with infinite delay ⋮ A uniform stability result for thermoelasticity of type III with boundary distributed delay ⋮ Global existence, asymptotic stability, and uniform attractors for non-autonomous thermoelastic systems with constant time delay ⋮ Stability of delay evolution equations with fading stochastic perturbations ⋮ Threshold Dynamics of an HIV-TB Co-infection Model with Multiple Time Delays ⋮ Exponential stabilisation and dissipativity analysis of semilinear parabolic systems ⋮ A survey on Navier-Stokes models with delays: existence, uniqueness and asymptotic behavior of solutions

Cites Work

• Exponential stability of nonlinear differential delay equations
• Representation and control of infinite dimensional systems. Volume I
• Attractors for 2D-Navier-Stokes models with delays
• Convergence of the Kato approximants for evolution equations involving functional perturbations
• Existence of solutions and Galerkin approximations for nonlinear functional evolution equations
• Asymptotic behavior of solutions to a class of Volterra integrodifferential equations
• On a semilinear Volterra integrodifferential equation
• An abstract nonlinear Volterra integrodifferential equation
• Introduction to functional differential equations
• Necessary and sufficient conditions of asymptotic mean square stability for stochastic linear difference equations
• Autonomous nonlinear functional differential equations and nonlinear semigroups
• Construction of Lyapunov functionals for stochastic hereditary systems: A survey of some recent results
• Existence and stability of solutions to partial functional-differential equations with delay
• Theory and applications of partial functional differential equations
• Functional differential equations and nonlinear semigroups in \(L^p\) spaces
• Construction of Lyapunov functionals for stochastic difference equations with continuous time
• Lyapunov functionals construction for stochastic difference second-kind Volterra equations with continuous time
• Asymptotic behaviour of two–dimensional Navier–Stokes equations with delays
• Existence, Stability, and Compactness in the α-Norm for Partial Functional Differential Equations
• Abstract Functional Differential Equations and Reaction-Diffusion Systems
• Existence and Stability for Partial Functional Differential Equations
• Asymptotic Stability for Abstract Nonlinear Functional Differential Equations
• Navier-Stokes equations with delays
• On the construction of methods of lines for functional evolutions in general Banach spaces
• Sur les perturbations des équations d'évolution : application à des problèmes de retard
• GENERAL METHOD OF LYAPUNOV FUNCTIONALS CONSTRUCTION IN STABILITY INVESTIGATIONS OF NONLINEAR STOCHASTIC DIFFERENCE EQUATIONS WITH CONTINUOUS TIME
• Nonlinear partial functional differential equations: Existence and stability
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Method of Lyapunov functionals construction in stability of delay evolution equations