Decay Solutions of Coupled Schr¨odinger Equation with Internal Fractional Damping

Decay Solutions of Coupled Schr¨odinger Equation with Internal Fractional Damping


  • Naima Louhibi, Khadidja Fekirini, Meradjah Ibrahim


Coupled Schr¨odinger equation, Internal fractional damping, semigroup theory, polynomial stability


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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How to Cite

Decay Solutions of Coupled Schr¨odinger Equation with Internal Fractional Damping. (2023). Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 01-14.