非线性时变薛定谔方程的部分数据逆问题

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Mathematical Analysis Pub Date : 2024-07-02 DOI:10.1137/23m1587993

Ru-Yu Lai, Xuezhu Lu, Ting Zhou

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷第 4 期，第 4712-4741 页，2024 年 8 月。摘要本文证明了从边界 Dirichlet-to-Neumann（DN）映射确定薛定谔方程[math]中随时间变化的非线性系数[math]的唯一性和稳定性。我们尤其对部分数据问题感兴趣，在这个问题中，DN 映射是在边界的适当子集上测量的。我们展示了两个结果：在某些类型的几何光学解可以达到的点上系数的局部唯一性，以及基于线性方程唯一延续性质的稳定性估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Partial Data Inverse Problems for the Nonlinear Time-Dependent Schrödinger Equation

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4712-4741, August 2024.
Abstract. In this paper we prove the uniqueness and stability in determining a time-dependent nonlinear coefficient [math] in the Schrödinger equation [math], from the boundary Dirichlet-to-Neumann (DN) map. In particular, we are interested in the partial data problem, in which the DN map is measured on a proper subset of the boundary. We show two results: a local uniqueness of the coefficient at the points where certain types of geometric optics solutions can reach, and a stability estimate based on the unique continuation property for the linear equation.

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.