Observability for the Schr\"odinger Equation: an Optimal Transport Approach

François Golse; Thierry Paul

Observability for the Schr\"odinger Equation: an Optimal Transport Approach

Analysis of PDEs 2021-02-11 v1

Authors: François Golse , Thierry Paul

Abstract

We establish an observation inequality for the Schr\"odinger equation on $\mathbf{R}^d$ , uniform in the Planck constant $\hbar\in[0,1]$ . The proof is based on the pseudometric introduced in [F. Golse, T. Paul, Arch. Rational Mech. Anal. 223 (2017), 57-94]. This inequality involves only effective constants which are computed explicitly in their dependence in $\hbar$ and all parameters involved.

Keywords

schrödinger equation observability inequality optimal transport planck constant pseudometric

Cite

@article{arxiv.2102.05155,
  title  = {Observability for the Schr\"odinger Equation: an Optimal Transport Approach},
  author = {François Golse and Thierry Paul},
  journal= {arXiv preprint arXiv:2102.05155},
  year   = {2021}
}

Comments

15 pages, no figure

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