Schock waves and compactons for fifth-order nonlinear dispersion equations. II

2009/11/23 by V. A. Galaktionov, Galaktionov, V. A.
Mathematics · #35K55 #35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35K55 #msc:35K65

paper · pdf · doi:10.48550/arxiv.0911.4446

48 pages, 23 figures

arxiv created 2009/11/23 · arxiv updated 2009/12/08

Abstract

It is shown that fifth-order nonlinear dispersion equations from compacton theory admit shock and rarefaction waves. A self-similar gradient blow-up is shown to admit infinitely many similarity extensions beyond blow-up time, meaning principal nonuniqueness of solutions of the Cauchy problem after occurring such singularities.

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