Stability of a Schrödinger equation with internal fractional damping

Ibrahim Meradjah, Naima Louhibi, Abbes Benaissa

Abstract


In this paper, we are concerned with the stabilization of a linear Schrödinger equation in an n-dimensional open bounded domain under Dirichlet boundary conditions with an internal fractional damping.
We reformulate the system into an augmented model and prove the well-posedness of it by using semigroup method.
Based on a general criteria of Arendt-Batty, we show that the system is strongly stable. 
By combining frequency domain method and multiplier techniques, we establish an optimal polynomial energy decay rate.




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References


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DOI: https://doi.org/10.52846/ami.v50i2.1739