Non-uniqueness of transonic shock solutions to Euler–Poisson system with varying background charges

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED
Ben Duan, Haoran Zheng
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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.
背景电荷变化的欧拉-泊松系统跨音速冲击解的非唯一性
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。
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来源期刊
CiteScore
1.70
自引率
10.00%
发文量
59
审稿时长
6 months
期刊介绍: Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.
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