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arXiv · 2601.01286

On the stability of degenerate Schr\"{o}dinger equation under boundary fractional damping

Fatiha Chouaou·Abbes Benaissa
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Abstract

In this paper we study the well-posedness and stability of degenerate Schr\"{o}dinger equation with a fractional boundary damping. First, we establish the well-posedness of the degenerate problem $\psi_t(x,t)-\imath(\tau(x) \psi_x(x,t))_x=0, \hbox{ with } x \in (0,1)$, controlled by Dirichlet-Neumann conditions. Then, exponential and polynomial decay rate of the solution are established using multiplier method.

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Fatiha Chouaou, Abbes Benaissa. 2026-01-03. On the stability of degenerate Schr\"{o}dinger equation under boundary fractional damping. https://arxiv.org/abs/2601.01286

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