Dodd, Jeff2021-08-172021-08-172007-10-13Dodd, 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. 1-13.1072-6691https://hdl.handle.net/10877/14349It 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.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalTravelling wavesUndercompressive shocksSpectral stabilityEvans functionArticle