Abstract: | For Ω a smooth domain in Rn with boundary Λ = Λ0Λ1, we are concerned with the wave equation y″ − Δy = S in QT =]0, T × Ω with = ∂/∂t, at source term satisfying S, S′ ε L1(0, T L2 (Ω)). A Dirichlet condition is imposed on Λ0 and we consider an absorbing condition ∂y/∂n + uy′ = 0 in 0, T] × gL1 where u is the control.parameter. We introduce the cost function. and using the Min-Max formulation of J we by-pasas the sensitivity analysis of u → y and obtain the gradient of J with a usual adjoint problem. We first present an abstract frame for this kind of problems. using the differentiability results of a Min-Max 1,2], which we very shortly deduce here, we show that the well posedness of the adjoint equation implies differentiability of the cost function governed by a linear well posed problem. |