Homogénéisation
Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria
It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...
Problèmes variationnels et théorie du potentiel non linéaire
Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria
It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...
Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects
In the setting of a real Hilbert space , we investigate the asymptotic behavior, as time goes to infinity, of trajectories of second-order evolution equations () + () + (()) + (()) = 0, where is the gradient operator of a convex differentiable potential function : ,: is a maximal monotone operator which is assumed to be-cocoercive, and > 0 is a damping parameter. Potential and non-potential effects are associated respectively...
Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects
In the setting of
a real Hilbert space , we investigate the asymptotic behavior, as time
Convergence of convex-concave saddle functions : applications to convex programming and mechanics
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