Memory boundary feedback stabilization for Schrödinger equations with variable coefficients - Abdesselam, Nawel; Melkemi, Khaled (Electronic Journal of Differential Equations, 2017)
First we consider the boundary stabilization of Schrödinger equations with constant coefficient memory feedback. This is done by using Riemannian geometry methods and the multipliers technique. Then we explore the stabilization limits of Schrödinger equations whose elliptical part has a variable coefficient. We established the exponential decay of solutions using the multipliers techniques. The introduction of dissipative boundary conditions of memory type allowed us to obtain an accurate estimate on the uniform rate of decay of the energy for Schrödinger equations.