On the ultimate energy bound of solutions to some forced second order evolution equations with a general nonlinear damping operator - Sorbonne Université Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

On the ultimate energy bound of solutions to some forced second order evolution equations with a general nonlinear damping operator

Alain Haraux
  • Fonction : Auteur
  • PersonId : 836471

Résumé

Under suitable growth and coercivity conditions on the nonlinear damping operator g which ensure non-resonance, we estimate the ultimate bound of the energy of the general solution to the equationüequation¨equationü(t) + Au(t) + g(˙ u(t)) = h(t), t ∈ R + , where A is a positive selfadjoint operator on a Hilbert space H and h is a bounded forcing term with values in H. In general the bound is of the form C(1 + ||h|| 4) where ||h|| stands for the L ∞ norm of h with values in H and the growth of g does not seem to play any role. If g behaves lie a power for large values of the velocity, the ultimate bound has a quadratic growth with respect to ||h|| and this result is optimal. If h is anti periodic, we obtain a much lower growth bound and again the result is shown to be optimal even for scalar ODEs.
Fichier principal
Vignette du fichier
UB-2017.pdf (138.82 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01577067 , version 1 (24-08-2017)

Identifiants

Citer

Alain Haraux. On the ultimate energy bound of solutions to some forced second order evolution equations with a general nonlinear damping operator. 2017. ⟨hal-01577067⟩
350 Consultations
155 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More