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

DOI10.1007/s00030-011-0120-7zbMath1258.65092OpenAlexW1983371046MaRDI QIDQ421136

Warwick Tucker, Gunilla Kreiss, Oswald Fogelklou

Publication date: 23 May 2012

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-011-0120-7

zbMATH Keywords

existenceartificial viscosityboundary value problemsEuler equationsnumerical verificationcomputer-assisted proofenclosuretraveling wave solutionfixed-point problems

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Algorithms with automatic result verification (65G20) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Packaged methods for numerical algorithms (65Y15)

Related Items

A posteriori error bounds for two point boundary value problems: a Green's function approach ⋮ Parameterization Method for Unstable Manifolds of Standing Waves on the Line ⋮ Computer-assisted proofs in PDE: a survey

Uses Software

• Matlab
• INTLAB

Cites Work

• Generalized solutions for the Euler equations in one and two dimensions
• Mathematical problems for the next century
• Existence of weak solutions of 2-D Euler equations with initial vorticity \(\omega_ 0\in L(\log^ +L)^ \alpha\) \((\alpha>0)\)
• A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem
• Rigorous numerics for partial differential equations: The Kuramoto-Sivashinsky equation
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