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Existence and Uniqueness of Solutions for a Quasilinear KdV Equation with Degenerate Dispersion
Author(s) -
Germain Pierre,
HarropGriffiths Benjamin,
Marzuola Jeremy L.
Publication year - 2019
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21828
Subject(s) - uniqueness , degenerate energy levels , korteweg–de vries equation , mathematics , dispersion (optics) , mathematical analysis , phenomenon , mathematical physics , physics , nonlinear system , quantum mechanics
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. © 2019 Wiley Periodicals, Inc.