Naima Louhibi, Khadidja Fekirini, Meradja Ibrahim
Laboratory of Analysis and Control of PDEs, Djillali Liabes University, P.O. Box 89, Sidi Bel Abbes 22000, Algeria
In this work, we study a coupled Schrödinger equation with an internal fractional damping. First, we reformulate the system into an augmented model and establish the existence of the solutions through the theory of semigroup. Then, we prove the strong stability using the theorem of Arendt–Batty. A polynomial decay of the energy is shown by applying the theorem of A. Borichev and Y. Tomilov. Finally, we show the optimality decay by proving the lack of exponential stability.
Keywords: Coupled Schrödinger equation; Internal fractional damping; Semigroup theory; Polynomial stability.
Louhibi, N., Fekirini, K., & Ibrahim, M. (2023). Decay solutions of coupled Schrödinger equation with internal fractional damping. Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 1–14.