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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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Linear Stability of Solitary Waves for the Isothermal Euler-Poisson System

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dc.contributor.author Bae, Junsik ko
dc.contributor.author Kwon, Bongsuk ko
dc.date.available 2021-12-16T07:59:25Z -
dc.date.created 2021-12-10 ko
dc.date.issued 2022-01 ko
dc.identifier.citation ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.243, pp.257 - 327 ko
dc.identifier.issn 0003-9527 ko
dc.identifier.uri https://scholarworks.unist.ac.kr/handle/201301/55135 -
dc.description.abstract We study the asymptotic linear stability of a two-parameter family of solitary waves for the isothermal Euler-Poisson system. When the linearized equations about the solitary waves are considered, the associated eigenvalue problem in L-2 space has a zero eigenvalue embedded in the neutral spectrum, i.e., there is no spectral gap. To resolve this issue, use is made of an exponentially weighted L-2 norm so that the essential spectrum is strictly shifted into the left-half plane, and this is closely related to the fact that solitary waves exist in the super-ion-sonic regime. Furthermore, in a certain long-wavelength scaling, we show that the Evans function for the Euler-Poisson system converges to that for the Korteweg-de Vries (KdV) equation as an amplitude parameter tends to zero, from which we deduce that the origin is the only eigenvalue on its natural domain with algebraic multiplicity two. We also show that the solitary waves are spectrally stable in L-2 space. Moreover, we discuss (in)stability of large amplitude solitary waves. ko
dc.language 영어 ko
dc.publisher SPRINGER ko
dc.title Linear Stability of Solitary Waves for the Isothermal Euler-Poisson System ko
dc.type ARTICLE ko
dc.identifier.scopusid 2-s2.0-85120033459 ko
dc.identifier.wosid 000723519100001 ko
dc.type.rims ART ko
dc.identifier.doi 10.1007/s00205-021-01722-8 ko
dc.identifier.url https://link.springer.com/article/10.1007%2Fs00205-021-01722-8 ko
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