Sharp estimates of bounded solutions to a second order forced equation with structural damping

Alain Haraux (1)

1 LJLL - Laboratoire Jacques-Louis Lions

By using differential inequalities, an essentially optimal L∞(R,D(A)) bound of the unique bounded solution of u″+cAu′=ƒ(t)is obtained wheneverA=A*≥λI is a bounded or unbounded linear operator on a real Hilbert space H and λ, c are positive constants, while ƒ ∈ L∞(R,H).

Domaines: Analyse fonctionnelle [math.FA]

Alain Haraux. Sharp estimates of bounded solutions to a second order forced equation with structural damping. 2006. ⟨hal-00112128⟩