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Kwon, Bongsuk
Partial Differential Equations and their applications
Research Interests
  • Partial differential equations, hyperbolic conservation laws, stability of nonlinear waves

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Quasi-neutral limit for Euler-Poisson system in the presence of boundary layers in an annular domain

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Title
Quasi-neutral limit for Euler-Poisson system in the presence of boundary layers in an annular domain
Author
Jung, Chang-YeolKwon, BongsukSuzuki, Masahiro
Issue Date
2020-11
Publisher
Academic Press
Citation
JOURNAL OF DIFFERENTIAL EQUATIONS, v.269, no.10, pp.8007 - 8054
Abstract
We investigate the quasi-neutral limit (the zero Debye length limit) for the Euler-Poisson system with radial symmetry in an annular domain. Under physically relevant conditions at the boundary, referred to as the Bohm criterion, we first construct the approximate solutions by the method of asymptotic expansion in the limit parameter, the square of the rescaled Debye length, whose detailed derivation and analysis are carried out in our companion paper [8]. By establishing -norm, , estimate of the difference between the original and approximation solutions, provided that the well-prepared initial data is given, we show that the local-in-time solution exists in the time interval, uniform in the quasi-neutral limit, and we prove the difference converges to zero with a certain convergence rate validating the formal expansion order. Our results mathematically justify the quasi-neutrality of a plasma in the regime of plasma sheath, indicating that a plasma is electrically neutral in bulk, whereas the neutrality may break down in a scale of the Debye length.
URI
https://scholarworks.unist.ac.kr/handle/201301/32381
URL
https://www.sciencedirect.com/science/article/pii/S0022039620303259
DOI
10.1016/j.jde.2020.06.011
ISSN
0022-0396
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