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

Alain Haraux (1)

1 LJLL - Laboratoire Jacques-Louis Lions

By using differential inequalities, a close-to-optimal L∞(ℝ,V) bound of the unique bounded solution of u"+cu'+Au=f(t) is obtained whenever A=A* ≥ I is a bounded or unbounded linear operator on a real Hilbert space H, V=D(A1/2) and λ,c> are positive constants, while f ∈ L∞(ℝ,H).

Domaines: Analyse numérique [math.NA]

Alain Haraux. Sharp estimates of bounded solutions to some second order forced dissipative equations. 2006. ⟨hal-00113444⟩