Existence and Uniqueness of Solutions for a Quasilinear KdV Equation with Degenerate Dispersion

Pierre Germain, Benjamin Harrop-Griffiths, Jeremy L. Marzuola

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Abstract

We consider a quasilinear KdV equation that admits compactly supported traveling wave solutions (compactons). This model is one of the most straightforward instances of degenerate dispersion, a phenomenon that appears in a variety of physical settings as diverse as sedimentation, magma dynamics and shallow water waves. We prove the existence and uniqueness of solutions with sufficiently smooth, spatially localized initial data.

Original languageEnglish (US)
JournalCommunications on Pure and Applied Mathematics
DOIs
StatePublished - Jan 1 2019

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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