How parabolic free boundaries approximate hyperbolic fronts

Brian H. Gilding, Roberto Natalini, Alberto Tesei

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    Abstract

    Some recent results concerning existence and qualitative behaviour of the boundaries of the suppurts of solutions of the Cauchy problem for nonlinear first-order hyperbolic and second-order parabolic scalar conservation laws are discussed. Among other properties, it is shown that, under appropriate assumptions, parabolic interfaces converge to hyperbolic ones in the vanishing viscosity limit.
    Original languageEnglish
    Pages (from-to)62-67
    Number of pages6
    JournalMemoirs on differential equations and mathematical physics
    Volume12
    Publication statusPublished - 1997

    Keywords

    • speed of propagation
    • shock waves
    • convection--diffusion equations
    • vanishing viscosity limit
    • EWI-16322
    • IR-70865
    • enthropy solutions
    • Conservation laws
    • METIS-140448

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