Finding the exact decay rate of all solutions to some second order evolution equations with dissipation - Laboratoire Jacques-Louis Lions Accéder directement au contenu
Article Dans Une Revue Journal of Functional Analysis Année : 2016

Finding the exact decay rate of all solutions to some second order evolution equations with dissipation

Marina Ghisi
  • Fonction : Auteur
  • PersonId : 942729
Massimo Gobbino
  • Fonction : Auteur
  • PersonId : 942730
Alain Haraux
  • Fonction : Auteur
  • PersonId : 836471

Résumé

We consider an abstract second order evolution equation with damping. The "elastic" term is represented by a self-adjoint nonnegative operator A with discrete spectrum, and the nonlinear term has order greater than one at the origin. We investigate the asymptotic behavior of solutions. We prove the coexistence of slow solutions and fast solutions. Slow solutions live close to the kernel of A, and decay as negative powers of t as solutions of the first order equation obtained by neglecting the operator A and the second order time-derivatives in the original equation. Fast solutions live close to the range of A and decay exponentially as solutions of the linear homogeneous equation obtained by neglecting the nonlinear terms in the original equation. The abstract results apply to semilinear dissipative hyperbolic equations

Dates et versions

hal-01448318 , version 1 (27-01-2017)

Identifiants

Citer

Marina Ghisi, Massimo Gobbino, Alain Haraux. Finding the exact decay rate of all solutions to some second order evolution equations with dissipation. Journal of Functional Analysis, 2016, 271 (9), pp.2359-2395. ⟨10.1016/j.jfa.2016.08.010⟩. ⟨hal-01448318⟩
114 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More