{"title":"Non-uniqueness of transonic shock solutions to Euler–Poisson system with varying background charges","authors":"Ben Duan, Haoran Zheng","doi":"10.4310/cms.2024.v22.n3.a7","DOIUrl":null,"url":null,"abstract":"The Euler–Poisson equations with varying background charges in finitely long flat nozzles are investigated, for which two and only two transonic shock solutions are constructed. In href{https://dx.doi.org/10.4310/CMS.2012.v10.n2.a1}{[\\textrm{T. Luo and Z.P. Xin, Commun. Math. Sci., 10:419–462, 2012}]}, Luo and Xin established the wellposedness of steady Euler–Poisson equations for the constant background charge. Motivated by their pioneering work and combined with the special physical character of semiconductor devices, we propose the transonic shock problem in which the density of the background charge is a piecewise constant function and its discontinuity is determined only by shock fronts. The existence and non-uniqueness of transonic shock solutions are obtained via the method of shock matching.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cms.2024.v22.n3.a7","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The Euler–Poisson equations with varying background charges in finitely long flat nozzles are investigated, for which two and only two transonic shock solutions are constructed. In href{https://dx.doi.org/10.4310/CMS.2012.v10.n2.a1}{[\textrm{T. Luo and Z.P. Xin, Commun. Math. Sci., 10:419–462, 2012}]}, Luo and Xin established the wellposedness of steady Euler–Poisson equations for the constant background charge. Motivated by their pioneering work and combined with the special physical character of semiconductor devices, we propose the transonic shock problem in which the density of the background charge is a piecewise constant function and its discontinuity is determined only by shock fronts. The existence and non-uniqueness of transonic shock solutions are obtained via the method of shock matching.
研究了有限长平喷嘴中背景电荷变化的欧拉-泊松方程，构建了两个且仅有两个跨音速冲击解。在 href{https://dx.doi.org/10.4310/CMS.2012.v10.n2.a1}{[textrm{T. Luo and Z.P. Xin, Commun. Math. Sci.在他们开创性工作的激励下，结合半导体器件的特殊物理特性，我们提出了跨音速冲击问题，其中背景电荷密度是一个片断恒定函数，其不连续性仅由冲击前沿决定。通过冲击匹配方法，我们得到了跨音速冲击解的存在性和非唯一性。
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.
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