Fixed points of a destabilized Kuramoto-Sivashinsky equation

Ferenc A. Bartha, Warwick Tucker

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

We consider the family of destabilized Kuramoto-Sivashinsky equations in one spatial dimension ut + νuxxxx + βuxx + γuux = αu for α, ν ≥ 0 and β, γ ∈ ℝ. For certain parameter values, shock-like stationary solutions have been numerically observed. In this work we verify the existence of several such solutions using the framework of self-consistent bounds and validated numerics.

Original languageEnglish
Pages (from-to)339-349
Number of pages11
JournalApplied Mathematics and Computation
Volume266
DOIs
Publication statusPublished - 1 Sep 2015
Externally publishedYes

Keywords

  • Boundary value problem
  • Galerkin projection
  • Interval arithmetic
  • Kuramoto-Sivashinsky equations
  • Rigorous computations
  • Self-consistent bounds

Cite this