Variational Approach to Complicated Similarity Solutions of Higher-Order Nonlinear PDEs. II

2011/03/14 by В. А. Галактионов, V. A. Galaktionov, Galaktionov, V. A. +4
Mathematics · Physics and Astronomy · #35K40 #35K55 #35K65 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #msc:35K40 #msc:35K55 #msc:35K65

paper · pdf · doi:10.48550/arxiv.1103.2643

48 pages, 26 figures

arxiv created 2011/03/14 · openalex publication_date 2011/03/14 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some higher-order quasilinear parabolic, hyperbolic, and nonlinear dispersion equations are shown to admit various blow-up, extinction, and travelling wave solutions, which reduce to variational problems admitting countable families of compactly supported solutions.

Related

• Variational approach to complicated similarity solutions pf higher-order nonlinear PDEs. I
• Third-order nonlinear dispersion PDEs: shocks, rarefaction, and blow-up waves
• Representation of Dissipative Solutions to a Nonlinear Variational Wave Equation
• Towards the KPP--Problem and log t-Front Shift for Higher-Order Nonlinear PDEs III. Dispersion and Hyperbolic Equations
• Nonlinear dispersion equations: smooth deformations, compactons, and extensions to higher orders