具有随时间变化的阻尼系数和电势的双曲线方程的部分数据反演问题

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-08-08 DOI:10.1137/23m1588676

Boya Liu, Teemu Saksala, Lili Yan

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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 5678-5722 页，2024 年 8 月。摘要。我们研究在三维或更高维度的紧凑黎曼流形中确定波方程中出现的随时间变化的阻尼系数和势的逆问题。更具体地说，我们关注保角横向各向异性流形的情况，或者换句话说，边界保角嵌入欧几里得线与横向流形的乘积的紧凑黎曼流形。我们还假定衰减大地射线变换在横向流形上是注入式的，从而证明了某个部分考奇数据集的知识唯一地决定了随时间变化的阻尼系数和势能。

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Partial Data Inverse Problem for Hyperbolic Equation with Time-Dependent Damping Coefficient and Potential

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5678-5722, August 2024.
Abstract. We study an inverse problem of determining a time-dependent damping coefficient and potential appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of conformally transversally anisotropic manifolds, or in other words, compact Riemannian manifolds with boundary conformally embedded in a product of the Euclidean line and a transversal manifold. With an additional assumption of the attenuated geodesic ray transform being injective on the transversal manifold, we prove that the knowledge of a certain partial Cauchy data set determines the time-dependent damping coefficient and potential uniquely.

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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.