Convergence to steady states of solutions of semilinear evolutionary integral equations

DOI10.1007/s00526-004-0278-5zbMath1087.45005OpenAlexW1991454863MaRDI QIDQ2575177

Eva Fašangová, Ralph Chill

Publication date: 8 December 2005

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-004-0278-5

zbMATH Keywords

bounded solutionsconvergence to steady state solutionsKelvin-Voigt solidsnonlinear evolution integral equationsviscoelastic Euler-Bernoulli beam

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Integro-partial differential equations (45K05) Other nonlinear integral equations (45G10) Abstract integral equations, integral equations in abstract spaces (45N05)

Related Items (13)

Asymptotic behavior of a nonisothermal viscous Cahn-Hilliard equation with inertial term ⋮ Convergence to equilibrium of solutions to a nonautonomous semilinear viscoelastic equation with finite or infinite memory ⋮ Asymptotic convergence of solutions to the forest kinematic model ⋮ Asymptotic stability of solutions to a semilinear viscoelastic equation with analytic nonlinearity ⋮ Convergence to steady states of solutions to nonlinear integral evolution equations ⋮ Long-time behavior of nonlinear integro-differential evolution equations ⋮ Well-posedness and asymptotic behavior of a nonautonomous, semilinear hyperbolic-parabolic equation with dynamical boundary condition of memory type ⋮ Asymptotic behavior of solutions for linear evolutionary boundary value problem of viscoelastic damped wave equation ⋮ Lyapunov functions and convergence to steady state for differential equations of fractional order ⋮ Two-dimensional reaction-diffusion equations with memory ⋮ Energy decay estimates of solutions for viscoelastic damped wave equations in \(\mathbb{R}^N\) ⋮ APPLICATIONS OF THE ŁOJASIEWICZ–SIMON, GRADIENT INEQUALITY TO GRADIENT-LIKE EVOLUTION EQUATIONS ⋮ \(L^p\)-maximal regularity for second order Cauchy problems

Cites Work

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• Convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity
• On the Łojasiewicz--Simon gradient inequality.
• Rate of decay to equilibrium in some semilinear parabolic equations.
• Convergence of bounded weak solutions of the wave equation with dissipation and analytic nonlinearity
• Asymptotic stability in viscoelasticity
• Compactness of bounded trajectories of dynamical systems in infinite dimensional spaces
• Evolutionary Integral Equations and Applications
• Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping
• Long-time stabilization of solutions to a phase-field model with memory
• Asymptotic behaviour of a semilinear viscoelastic beam model

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