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


Stability of planar shock fronts for multidimensional systems of relaxation equations

DC Field Value Language Kwon, Bongsuk ko 2014-11-14T00:09:32Z - 2014-11-12 ko 2011-10 ko
dc.identifier.citation JOURNAL OF DIFFERENTIAL EQUATIONS, v.251, no.8, pp.2226 - 2261 ko
dc.identifier.issn 0022-0396 ko
dc.identifier.uri -
dc.description.abstract We investigate stability of multidimensional planar shock profiles of a general hyperbolic relaxation system whose equilibrium model is a system, under the necessary assumption of spectral stability and a standard set of structural conditions that are known to hold for many physical systems. Our main result, generalizing the work of Kwon and Zumbrun in the scalar relaxation case, is to establish the bounds on the Green's function for the linearized equation and obtain nonlinear L2 asymptotic behavior/sharp decay rate of perturbed weak shock profiles. To establish Green's function bounds, we use the semigroup approach in the low-frequency regime, and use the energy method for the high-frequency bounds, separately. For the system equilibrium case, the analysis of the linearized equation is complicated due to glancing phenomena. We treat this difficulty similarly as in the inviscid and viscous systems, under the constant multiplicity condition. ko
dc.description.statementofresponsibility close -
dc.language 영어 ko
dc.title Stability of planar shock fronts for multidimensional systems of relaxation equations ko
dc.type ARTICLE ko
dc.identifier.scopusid 2-s2.0-79960907717 ko
dc.identifier.wosid 000294084800011 ko
dc.type.rims ART ko
dc.description.wostc 0 *
dc.description.scopustc 0 * 2015-05-06 * 2014-11-12 *
dc.identifier.doi 10.1016/j.jde.2011.07.007 ko
dc.identifier.url ko
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