On the controllability of an interior set degenerate Schrödinger equation

Mohamed Alahyane, Abderrazak Chrifi and Younes Echarroudi

Mathematische Nachrichten, 2025, vol. 298, issue 2, 644-676

Abstract: In this paper, we are interested on the null controllability property of a linear degenerate Schrödinger equation with a degeneracy occurring on an interior subset of (0,1),that is,∃W1⊂⊂(0,1),such that∀x∈W1,k(x)=0$(0,1), \text{ that is, } \exists W_{1}\subset \subset (0,1), \text{ such that } \forall x\in W_{1}, \text{ } k(x)=0$, where k$k$ stands for the quantum diffusion. More precisely, we are concerned with the null controllability phenomenon using the classical procedure founded on a new Carleman estimate and afterward a newfangled observability inequality.

Date: 2025
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