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

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

doi:10.1002/cpa.21828

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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	2449-2484
Number of pages	36
Journal	Communications on Pure and Applied Mathematics
Volume	72
Issue number	11
DOIs	https://doi.org/10.1002/cpa.21828
State	Published - Nov 1 2019

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/cpa.21828

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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.",

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AB - 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.

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

Abstract

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