A computer-assisted proof of the existence of traveling wave solutions to the scalar Euler equations with artificial viscosity

Oswald Fogelklou, Warwick Tucker, Gunilla Kreiss

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


We establish the existence and local uniqueness of traveling wave solutions to the one-dimensional Euler equations with artificial viscosity. The equations are expressed as a fixed-point problem, which is solved by a computer-assisted method based on Yamamoto's application of the Banach fixed-point theorem.

Original languageEnglish
Pages (from-to)97-131
Number of pages35
JournalNonlinear Differential Equations and Applications
Issue number1
Publication statusPublished - 1 Feb 2012
Externally publishedYes


  • Boundary value problems
  • Computer-assisted proof
  • Enclosure
  • Euler equations
  • Existence
  • Fixed-point problems
  • Numerical verification

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