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On the controllability of an interior set degenerate Schrödinger equation

Author

Listed:
  • Mohamed Alahyane
  • Abderrazak Chrifi
  • Younes Echarroudi

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.

Suggested Citation

  • Mohamed Alahyane & Abderrazak Chrifi & Younes Echarroudi, 2025. "On the controllability of an interior set degenerate Schrödinger equation," Mathematische Nachrichten, Wiley Blackwell, vol. 298(2), pages 644-676, February.
    • Handle: RePEc:bla:mathna:v:298:y:2025:i:2:p:644-676
    DOI: 10.1002/mana.202300252
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