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Title of Journal: J Dyn Diff Equat

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Abbravation: Journal of Dynamics and Differential Equations

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Springer US

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DOI

10.1007/bf00449063

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ISSN

1572-9222

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Existence and Asymptotic Behavior of Solutions to

Authors: Hassan Yassine
Publish Date: 2012/07/10
Volume: 24, Issue: 3, Pages: 645-661
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Abstract

Our aim in this article is to study a nonautonomous semilinear wave equation with nonlinear damping and dynamical boundary condition First we prove the existence and uniqueness of global bounded solutions having relatively compact range in the natural energy space Then by deriving an appropriate Lyapunov energy we show that if the exponent in the ŁojasiewiczSimon inequality is large enough depending on the damping then weak solutions converge to equilibrium

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Other Papers In This Journal:
  1. Basic Reproduction Ratios for Periodic Compartmental Models with Time Delay
  2. A Grobman–Hartman Theorem for Control Systems
  3. Invariant Tori of Full Dimension for Second KdV Equations with the External Parameters
  4. Second Order Abstract Neutral Functional Differential Equations
  5. Complete Global and Bifurcation Analysis of a Stoichiometric Predator–Prey Model
  6. Existence of Rotating Spots with Spatially Dependent Feedback in the Plane in a Wave Front Interaction Model
  7. A Permutation Related to Non-compact Global Attractors for Slowly Non-dissipative Systems
  8. Random Attractor Associated with the Quasi-Geostrophic Equation
  9. A Free Boundary Problem for the Predator–Prey Model with Double Free Boundaries
  10. Stability of Solitary Waves for the Generalized Higher-Order Boussinesq Equation
  11. A Few Remarks on Partially Hyperbolic Diffeomorphisms of $${\mathbb T}^3$$ Isotopic to Anosov
  12. On The Number of Characteristic Lines for Homogeneous Vector Fields
  13. Eigenvalues of Self-Similar Solutions of the Dafermos Regularization of a System of Conservation Laws via Geometric Singular Perturbation Theory
  14. Real Analytic Quasi-Periodic Solutions with More Diophantine Frequencies for Perturbed KdV Equations
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