Asymptotic Analysis

In this article, we investigate the existence of ground state solutions for the following generalized Schrödinger–Poisson system: { − Δ u + u + κ ϕ g ( u ) = f ( u ) , in  R 3 , − Δ ϕ = G ( u ) , in  R 3 , where κ > 0 is a parameter, g = G ′ ∈ C ( R , R ) , and f ∈ C ( R , R ) . By combining the monotonicity trick with refined variational and analytical techniques, we establish the existence of ground state solutions for the above system under mild assumptions on f and g .

In this article, we propose a new numerical strategy for the stabilization of evolution systems. The method is based on the methodology given by Ammari–Nicaise–Pignotti in Ammari et al. This method is then implemented in one-dimensional by suitable numerical approximation techniques. Numerical experiments complete this study to confirm the theoretically announced results.

In this article, we investigate the boundary optimal control problem associated with Heat equation in a two-dimensional highly oscillating domain Ω ϵ in which the control is applied periodically via Neumann condition on the oscillating part of the boundary. We characterize the optimal control in terms of unfolding operator and then study the homogenization to obtain two limit optimal control problems depending on the scalar parameters. In the limit optimal control problem, we obtain three controls, namely interior control, an interfacial control and a boundary control.