具有时空非局部衰减的双曲方程中多种时间依赖系数的同时恢复

中文摘要 AI 辅助

本文致力于研究具有时空非局部衰减的双曲方程中，从局部源到解的映射唯一确定不同类别系数的反问题。我们的目标是利用非局部衰减机制来解决在没有衰减的线性和非线性双曲方程中仍然开放甚至根本难以处理的反系数问题。更确切地说，通过利用非局部衰减引起的相互作用，我们同时确定同时依赖于空间和时间的一般类别的首项和低阶系数。此外，我们使用在不相交集上收集的数据来表述我们的结果，从而扩展了现有理论，并引入了双曲方程在空间和时间上都不相交的数据集的概念。我们的方法建立在非局部算子的关键特征之上，例如记忆效应和唯一延拓原理，同时整合了局部与非局部算子之间的相互作用以及双曲方程的结构性质。

英文摘要

This article is devoted to the inverse problem of uniquely determining different classes of coefficients in a hyperbolic equation with space-time nonlocal attenuation from a local source-to-solution map. Our objective is to exploit the nonlocal attenuation mechanism to address inverse coefficient problems that remain open, or are even fundamentally intractable, for linear and nonlinear hyperbolic equations without attenuation. More precisely, by leveraging the interactions induced by nonlocal attenuation, we simultaneously determine general classes of leading and lower order coefficients depending on both space and time. In addition, we formulate our results using data collected on disjoint sets, thereby extending the existing theory and introducing the notion of data on sets disjoint in both space and time for hyperbolic equations. Our approach builds on key features of nonlocal operators, such as memory effects and the unique continuation principle, while integrating the interplay between local and nonlocal operators along with structural properties of hyperbolic equations.

发表机构

• Univ Rouen Normandie, CNRS, Normandie Univ, LMRS UMR 6085（鲁昂诺曼底大学）
• Department of Mathematics, University of Washington（华盛顿大学数学系）

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