恢复半线性传输方程中的系数

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED Archive for Rational Mechanics and Analysis Pub Date : 2024-06-19 DOI:10.1007/s00205-024-02007-6

Ru-Yu Lai, Gunther Uhlmann, Hanming Zhou

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引用次数: 0

摘要

我们考虑了与时间相关的半线性传输方程的逆问题。我们证明，通过对线性传输方程应用线性化方案和卡勒曼估计，线性项（吸收或散射系数）和非线性项中与时间无关的系数可以通过稳定的边界测量唯一确定。我们在欧几里得和一般几何设置中都建立了结果。

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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Recovery of Coefficients in Semilinear Transport Equations

We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a stable way, from the boundary measurements, by applying a linearization scheme and Carleman estimates for the linear transport equations. We establish results in both Euclidean and general geometry settings.

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.