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<div class="csl-entry">Achleitner, F. G. (2009). <i>Bifurcation and stability of viscous shock waves in viscous conservation laws</i> [Dissertation, Technische Universität Wien]. reposiTUm. https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-26281</div>
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It is a natural idea to study the stability of shock waves by analyzing the spectrum of the linearized evolution operator. The Evans function approach to such problems provides a general geometric framework to study and exploit spectral properties of the linearized problem. Briefly speaking, the Evans function is an analytic function of the spectral parameter whose zeros to the right of the essential spectrum correspond to eigenvalues. A shock wave is spectrally stable, if the spectrum of the related linear operator consists of eigenvalues with negative real part and the eigenvalue zero. Zumbrun and collaborators have shown that spectral stability of viscous shock wave implies its nonlinear stability.<br />We study the generic case of a saddle-node bifurcation of viscous shock waves, where the family of viscous shock waves can be described via the Melnikov function. By relating the derivatives of the Melnikov function with derivatives of the Evans function, we prove a change of stability within the family of viscous shock waves. We apply our results to an example in magnetohydrodynamics.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Evans Funktion
de
dc.subject
viskose Erhaltungsgleichungen
de
dc.subject
viskose Schockwellen
de
dc.subject
spektrale Stabilität
de
dc.subject
Melnikov Funktion
de
dc.subject
Evans function
en
dc.subject
viscous conservation laws
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dc.subject
viscous shock waves
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dc.subject
spectral stability
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dc.subject
Melnikov function
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dc.title
Bifurcation and stability of viscous shock waves in viscous conservation laws
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dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
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dc.rights.license
Urheberrechtsschutz
de
dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Franz Achleitner
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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dc.contributor.assistant
Freistühler, Heinrich
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tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing