Sharp estimates of bounded solutions to some semilinear second order dissipative equations

Cyrine Fitouri (1) , Alain Haraux (1)

1 LJLL - Laboratoire Jacques-Louis Lions

Let H,V be two real Hilbert spaces such that H ⊂ V with continuous and dense imbedding, and let F ∈ C¹(V) be convex. By using differential inequalities, a close-to-optimal ultimate bound of the energy is obtained for solutions in C¹(ℝ⁺,V) ∩ W^2,∞_loc(ℝ⁺,V^’)u” + cu&rsquo + bu + ∇F(u) = ƒ(t) whenever ƒ ∈ L^∞(ℝ,H).

Mots clés: second order equation; bounded solution

Domaines: Analyse numérique [math.NA]

Cyrine Fitouri, Alain Haraux. Sharp estimates of bounded solutions to some semilinear second order dissipative equations. 2007. ⟨hal-00171972⟩