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

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

Research output: Contribution to journalArticle

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)
Pages (from-to)2449-2484
Number of pages36
JournalCommunications on Pure and Applied Mathematics
Volume72
Issue number11
DOIs
StatePublished - Nov 1 2019

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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