Decay Solutions of Coupled Schr¨odinger Equation with Internal Fractional Damping
Keywords:
Coupled Schr¨odinger equation, Internal fractional damping, semigroup theory, polynomial stabilityAbstract
In this work, we study a coupled Schr¨odinger equation with an internal fractional damping. First, we reformulate the system into an augmented model and we 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.
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