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

Germain Pierre | Zendy; HarropGriffiths Benjamin | Zendy; Marzuola Jeremy L. | Zendy

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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.

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