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arXiv · 2509.05533

Stability of Degenerate Schr\"{o}dinger Equation with Harmonic Method

Khadidja Fekirini·Naima Louhibi·Abbes Benaissa
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Abstract

This paper is devoted to study the well-posedness and stability of degenerate Schr\"{o}dinger equation with a boundary control acting at the degeneracy. First, we establish the well-posedness of the degenerate problem $v_t(x,t)+\imath(x^\alpha v_x(x,t))_x=0, \hbox{ with } x \in (0,1)$, controlled by Dirichlet-Neumann conditions. Then, exponential and polynomial decreasing of the solution are established. This result is optimal and it is obtained using complex analysis method.

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Khadidja Fekirini, Naima Louhibi, Abbes Benaissa. 2025-09-05. Stability of Degenerate Schr\"{o}dinger Equation with Harmonic Method. https://arxiv.org/abs/2509.05533

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