Third-order nonlinear dispersion PDEs: shocks, rarefaction, and blow-up waves

Abstract

Various shock and rarefaction-type similarity solutions of the third-order nonlinear dispersion equation in 1D are constructed. Blow-up of some solutions are proved by different techniques.

32 pages, 12 figures

References in corpus (1)

• Formation of shocks in higher-order nonlinear dispersion PDEs: nonuniqueness and nonexistence of entropy

Cited by in corpus (7)

• 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
• Nonlinear dispersion equations: smooth deformations, compactons, and extensions to higher orders
• Very Singular Similarity Solutions and Hermitian Spectral Theory for Semilinear Odd-Order PDEs
• Schock waves and compactons for fifth-order nonlinear dispersion equations. II
• On blow-up shock waves for a nonlinear PDE associated with Euler equations
• On self-similar collapse of discontinuous data for thin film equations with doubly degenerate mobility