Scholarlink

<p>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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

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

  • 期刊论文

  • 发表日期：

    2025年5月30日

查看全文
  • Salah-Eddine Chorfi,
  • Alemdar Hasanov,
  • Roberto Morales

摘要

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.