L-2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws
DC Field | Value | Language |
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dc.contributor.author | Kang, Moon-Jin | - |
dc.contributor.author | Vasseur, Alexis F. | - |
dc.contributor.author | Wang, Yi | - |
dc.date.available | 2021-02-22T05:46:07Z | - |
dc.date.issued | 2019-08 | - |
dc.identifier.issn | 0022-0396 | - |
dc.identifier.issn | 1090-2732 | - |
dc.identifier.uri | https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/2917 | - |
dc.description.abstract | We consider a L-2-contraction (a L-2-type stability) of large viscous shock waves for the multidimensional scalar viscous conservation laws, up to a suitable shift by using the relative entropy methods. Quite different from the previous results, we find a new way to determine the shift function, which depends both on the time and space variables and solves a viscous Hamilton-Jacobi type equation with source terms. Moreover, we do not impose any conditions on the anti-derivative variables of the perturbation around the shock profile. More precisely, it is proved that if the initial perturbation around the viscous shock wave is suitably small in L-2-norm, then the L-2-contraction holds true for the viscous shock wave up to a suitable shift function. Note that BY-norm or the L-infinity-norm of the initial perturbation and the shock wave strength can be arbitrarily large. Furthermore, as the time t tends to infinity, the L-2-contraction holds true up to a (spatially homogeneous) time-dependent shift function. In particular, if we choose some special initial perturbations, then L-2-convergence of the solutions towards the associated shock profile can be proved up to a time-dependent shift. (C) 2019 Elsevier Inc. All rights reserved. | - |
dc.format.extent | 55 | - |
dc.language | 영어 | - |
dc.language.iso | ENG | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.title | L-2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws | - |
dc.type | Article | - |
dc.publisher.location | 미국 | - |
dc.identifier.doi | 10.1016/j.jde.2019.03.030 | - |
dc.identifier.scopusid | 2-s2.0-85063692191 | - |
dc.identifier.wosid | 000468614700002 | - |
dc.identifier.bibliographicCitation | JOURNAL OF DIFFERENTIAL EQUATIONS, v.267, no.5, pp 2737 - 2791 | - |
dc.citation.title | JOURNAL OF DIFFERENTIAL EQUATIONS | - |
dc.citation.volume | 267 | - |
dc.citation.number | 5 | - |
dc.citation.startPage | 2737 | - |
dc.citation.endPage | 2791 | - |
dc.type.docType | Article | - |
dc.description.isOpenAccess | N | - |
dc.description.journalRegisteredClass | sci | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordPlus | NAVIER-STOKES EQUATIONS | - |
dc.subject.keywordPlus | FLUID DYNAMIC LIMITS | - |
dc.subject.keywordPlus | RELATIVE ENTROPY | - |
dc.subject.keywordPlus | NONLINEAR STABILITY | - |
dc.subject.keywordPlus | BOLTZMANN-EQUATION | - |
dc.subject.keywordPlus | KINETIC-EQUATIONS | - |
dc.subject.keywordPlus | RIEMANN SOLUTIONS | - |
dc.subject.keywordPlus | ASYMPTOTIC STABILITY | - |
dc.subject.keywordPlus | EULER EQUATIONS | - |
dc.subject.keywordPlus | FOURIER SYSTEM | - |
dc.identifier.url | https://www.sciencedirect.com/science/article/abs/pii/S002203961930138X?via%3Dihub | - |
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