Determination of Source Terms in Diffusion and Wave Equations by Observations After Incidents: Uniqueness and Stability

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2021-07-17 DOI:10.4208/csiam-am.so-2022-0028

Jin Cheng, Shuai Lu, Masahiro Yamamoto

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引用次数: 2

Abstract

We consider a diffusion and a wave equations: $$ \partial_t^ku(x,t) = \Delta u(x,t) + \mu(t)f(x), \quad x\in \Omega, \, t>0, \quad k=1,2 $$ with the zero initial and boundary conditions, where $\Omega \subset \mathbb{R}^d$ is a bounded domain. We establish uniqueness and/or stability results for inverse problems of 1. determining $\mu(t)$, $0

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通过事故后观测确定扩散方程和波动方程中的源项：唯一性和稳定性

我们考虑具有零初始和边界条件的扩散和波动方程：$$\partial_t^ku（x，t）=\Delta u（x，t）+\mu（t）f（x），\quad x\in\Omega，\，t>0，\ quad k=1,2$$，其中$\Omega\subet\mathbb｛R｝^d$是有界域。我们建立了1的反问题的唯一性和/或稳定性结果。用给定的$f（x）$确定$\mu（t）$，$0

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.