Spectral stability of undercompressive shock profile solutions of a modified KdV-Burgers equation

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dc.contributor.authorDodd, Jeff
dc.date.accessioned2021-08-17T18:31:10Z
dc.date.available2021-08-17T18:31:10Z
dc.date.issued2007-10-13
dc.description.abstractIt is shown that certain undercompressive shock profile solutions of the modified Korteweg-de Vries-Burgers equation ∂tu + ∂x(u3) = ∂3xu + α∂2xu, α ≥ 0 are spectrally stable when α is sufficiently small, in the sense that their linearized perturbation equations admit no eigenvalues having positive real part except a simple eigenvalue of zero (due to the translation invariance of the linearized perturbation equations). This spectral stability makes it possible to apply a theory of Howard and Zumbrun to immediately deduce the asymptotic orbital stability of these undercompressive shock profiles when α is sufficiently small and positive.
dc.description.departmentMathematics
dc.formatText
dc.format.extent13 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationDodd, J. (2007). Spectral stability of undercompressive shock profile solutions of a modified KdV-Burgers equation. <i>Electronic Journal of Differential Equations, 2007</i>(135), pp. 1-13.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14349
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectTravelling waves
dc.subjectUndercompressive shocks
dc.subjectSpectral stability
dc.subjectEvans function
dc.titleSpectral stability of undercompressive shock profile solutions of a modified KdV-Burgers equation
dc.typeArticle

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