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    Nonlinear Stability of Periodic Traveling Wave Solutions of Viscous Conservation Laws in Dimensions One and Two

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    JohnsonM_SAIMJoAD_10(1)189.pdf (362.3Kb)
    Issue Date
    2011-01-01
    Author
    Johnson, Mathew A.
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
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    Abstract
    Extending results of Oh and Zumbrun in dimensions $d\geq3$, we establish nonlinear stability and asymptotic behavior of spatially periodic traveling-wave solutions of viscous systems of conservation laws in critical dimensions $d=1,2$, under a natural set of spectral stability assumptions introduced by Schneider in the setting of reaction diffusion equations. The key new steps in the analysis beyond that in dimensions $d\geq3$ are a refined Green function estimate separating off translation as the slowest decaying linear mode and a novel scheme for detecting cancellation at the level of the nonlinear iteration in the Duhamel representation of a modulated periodic wave.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1137/100781808.
    URI
    http://hdl.handle.net/1808/16912
    DOI
    https://doi.org/10.1137/100781808
    Collections
    • Mathematics Scholarly Works [282]
    Citation
    Johnson, Mathew A. & Zumbrun, Kevin. "Nonlinear Stability of Periodic Traveling Wave Solutions of Viscous Conservation Laws in Dimensions One and Two." SIAM J. Appl. Dyn. Syst., 10(1), 189–211. (23 pages). http://dx.doi.org/10.1137/100781808.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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