Recovery of a general nonlinearity in the semilinear wave equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-02 DOI:10.3233/asy-231890

Antônio Sá Barreto, Plamen Stefanov

引用次数: 0

Abstract

We study the inverse problem of recovery a nonlinearity f(t,x,u), which is compactly supported in x, in the semilinear wave equation utt−Δu+f(t,x,u)=0. We probe the medium with either complex or real-valued harmonic waves of wavelength ∼h and amplitude ∼1. They propagate in a regime where the nonlinearity affects the subprincipal but not the principal term, except for the zeroth harmonics. We measure the transmitted wave when it exits suppxf. We show that one can recover f(t,x,u) when it is an odd function of u, and we can recover α(x) when f(t,x,u)=α(x)u2m. This is done in an explicit way as h→0.

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半线性波方程中一般非线性的恢复

我们研究在半线性波方程 utt-Δu+f(t,x,u)=0 中恢复非线性 f(t,x,u)的逆问题。我们用波长 ∼h 和振幅 ∼1 的复值或实值谐波探测介质，它们在非线性影响次主项而不影响主项（三次谐波除外）的情况下传播。我们测量了传播波从 suppxf 流出时的情况。我们证明，当 f(t,x,u) 是 u 的奇函数时，我们可以恢复 f(t,x,u)；当 f(t,x,u)=α(x)u2m 时，我们可以恢复 α(x)。这可以通过 h→0 的显式方法实现。

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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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.