Boundedness and stability for the damped and forced single well Duffing equation

Cyrine Fitouri (1) , Alain Haraux (1)

1 LJLL - Laboratoire Jacques-Louis Lions

By using differential inequalities we improve some estimates of W.S. LOUD for the ultimate bound and asymptotic stability of the solutions to the Duffing equation u'' + cu' + g(u) = f(t) where c > 0, f is measurable and essentially bounded, and g is continuously differentiable with g' >= b > 0.

Domaines: Analyse classique [math.CA]; Systèmes dynamiques [math.DS]

Cyrine Fitouri, Alain Haraux. Boundedness and stability for the damped and forced single well Duffing equation. Discrete and Continuous Dynamical Systems - Series A, 2012, 33 (1), pp.211-223. ⟨10.3934/dcds.2013.33.211⟩. ⟨hal-01448178⟩