Convergence to steady states of solutions to nonlinear integral evolution equations

DOI10.1007/s00526-010-0342-2zbMath1213.37108OpenAlexW2016273167MaRDI QIDQ629851

Vicente Vergara

Publication date: 10 March 2011

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

Full work available at URL: https://doi.org/10.1007/s00526-010-0342-2

zbMATH Keywords

mild solutionsLyapunov functional\(\omega\)-limit setbounded solutionsequilibrium stateintegral evolution equation

Mathematics Subject Classification ID

Volterra integral equations (45D05) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05) Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian (35K91)

Related Items (4)

Long-time behavior of nonlinear integro-differential evolution equations ⋮ The KPP-problem and \(\log t\)-front shift for higher-order semilinear parabolic equations ⋮ On evolutionary Volterra equations with state-dependent delay ⋮ Regularity theory for a nonlinear fractional reaction-diffusion equation

Cites Work

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• Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
• Maximal regularity of type \(L_p\) for abstract parabolic Volterra equations
• A conserved phase field system with memory and relaxed chemical potential
• Convergence to equilibrium for second order differential equations with weak damping of memory type
• An analysis of a phase field model of a free boundary
• Convergence in gradient-like systems with applications to PDE
• Convergence of solutions of one-dimensional semilinear parabolic equations
• On the local structure of \(\omega\)-limit sets of maps
• A simple unified approach to some convergence theorems of L. Simon
• On the Łojasiewicz--Simon gradient inequality.
• A phase field system with memory: Global existence
• Asymptotic behaviour of solutions of a conserved phase-field system with memory
• Long-time behaviour and convergence towards equilibria for a conserved phase field model.
• Convergence to equilibrium for the Cahn-Hilliard equation with dynamic boundary conditions
• Well-posedness and long-time behaviour for the non-isothermal Cahn-Hilliard equation with memory
• Maximal regularity and global well-posedness for a phase field system with memory
• Lyapunov functions and convergence to steady state for differential equations of fractional order
• Convergence to steady states of solutions of semilinear evolutionary integral equations
• Completely positive measures and Feller semigroups
• Long-time convergence of solutions to a phase-field system
• Phase Field Equations with Memory: The Hyperbolic Case
• Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions
• Convergence of solutions to cahn-hilliard equation
• Evolutionary Integral Equations and Applications
• Operator-Valued Fourier Multipliers, Vector - Valued Besov Spaces, and Applications
• ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
• Long-time stabilization of solutions to a phase-field model with memory
• Convergence in gradient-like systems which are asymptotically autonomous and analytic
• Asymptotic behaviour of a semilinear viscoelastic beam model

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