Identification of source terms in the Schrödinger equation with dynamic boundary conditions from final data

Chorfi S., Hasanov A., Morales R.

Zeitschrift fur Angewandte Mathematik und Physik, vol.76, no.3, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 76 Issue: 3
  • Publication Date: 2025
  • Doi Number: 10.1007/s00033-025-02505-x
  • Journal Name: Zeitschrift fur Angewandte Mathematik und Physik
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Dynamic boundary condition, Fréchet gradient, Inverse problem, Landweber iteration, Schrödinger equation
  • Kocaeli University Affiliated: Yes

Abstract

In this paper, we study an inverse problem of retrieving two spatial–temporal source terms in the Schrödinger equation with dynamical boundary conditions from the final time overdetermination. We adopt a weak solution approach to solve the inverse source problem. By analyzing the associated Tikhonov functional, we prove an explicit formula for the functional gradient via the solution to a suitable adjoint backward system, allowing us to obtain the Lipschitz continuity of the gradient. Then, the existence and uniqueness of a quasi-solution are also investigated. Finally, our theoretical results are illustrated by numerical experiments in one dimension using the Landweber iteration method.