A Priori Bounds for Elastic Scattering by Deterministic and Random Unbounded Rough Surfaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-02-25 DOI:10.4208/csiam-am.so-2023-0001

Tianjiao Wang, Yi-Jhou Lin, Xiang-Yang Xu

引用次数: 0

Abstract

This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, which both are assumed to be graphs of Lipschitz continuous functions. For the deterministic case, an a priori bound explicitly dependent on frequencies is derived by the variational approach. For the scattering by random rough surfaces with a random source, well-posedness of the corresponding variation problem is proved. Moreover, a similar bound with explicit dependence on frequencies for the random case is also established based upon the deterministic result, Pettis measurability theorem and Bochner's integrability Theorem.

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确定性和随机无界粗糙表面弹性散射的先验界

本文研究了无界确定性粗糙表面和随机粗糙表面的弹性散射，假设这两个粗糙表面都是Lipschitz连续函数的图。对于确定性情况，通过变分方法导出了显式依赖于频率的先验界。对于具有随机源的随机粗糙表面的散射，证明了相应变分问题的适定性。此外，基于确定性结果、Pettis可测性定理和Bochner可积性定理，还建立了随机情况下显式依赖于频率的相似界。

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.