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

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.

48 pages, 23 figures

References in corpus (5)

• Wave-breaking and generic singularities of nonlinear hyperbolic equations
• Variational approach to complicated similarity solutions pf higher-order nonlinear PDEs. I
• Formation of shocks in higher-order nonlinear dispersion PDEs: nonuniqueness and nonexistence of entropy
• Third-order nonlinear dispersion PDEs: shocks, rarefaction, and blow-up waves
• Nonlinear dispersion equations: smooth deformations, compactons, and extensions to higher orders

Cited by in corpus (3)

• Formation of shocks in higher-order nonlinear dispersion PDEs: nonuniqueness and nonexistence of entropy
• On blow-up shock waves for a nonlinear PDE associated with Euler equations
• On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation I. Local oscillatory properties