Cavalcanti, Marcelo M.Correa, Wellington J.Özsarı, TurkerSepulveda, MauricioVejar Asem, Rodrigo2024-07-122024-07-122019Cavalcanti, M. M., Correa, W. J., Özsarı, T., Sepulveda, M., Vejar Asem, R. (2019). Exponential stability for the nonlinear Schrödinger equation with locally distributed damping. International Conference of Mathematical Sciences (ICMS 2019). s. 6.978-605-2124-29-1https://hdl.handle.net/20.500.12415/2184This talk is concerned with the defocusing nonlinear Schr¨odinger equation with a locally distributed damping on a smooth bounded domain. We first construct approximate solutions for this model by using the theory of monotone operators. We show that these approximate solutions decay exponentially fast in the L 2 -sense by using the multiplier technique and a unique continuation property. Then, we prove the global existence as well as the L 2 -decay of solutions for the original model by passing to the limit and using a weak lower semicontinuity argument, respectively. Finally, we implement a precise and efficient algorithm for studying the exponential decay established in the first part of the paper numerically. Our simulations illustrate the efficacy of the proposed control design.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessSchrödinger equationExponential stabilityLocally distributed dampingArticle66